9903:
12658:
31:
12644:
9747:
9151:
8835:
12682:
4317:
12670:
9195:
8894:
8586:
3940:
9742:{\displaystyle {\begin{aligned}P(X_{(k)}=x)&=P(X_{(k)}\leq x)-P(X_{(k)}<x),\\&=\sum _{j=0}^{n-k}{n \choose j}\left(p_{3}^{j}(p_{1}+p_{2})^{n-j}-(p_{2}+p_{3})^{j}(p_{1})^{n-j}\right),\\&=\sum _{j=0}^{n-k}{n \choose j}\left((1-F(x))^{j}(F(x))^{n-j}-(1-F(x)+f(x))^{j}(F(x)-f(x))^{n-j}\right).\end{aligned}}}
8194:
based approaches, the tuning parameter for the order statistic based density estimator is the size of sample subsets. Such an estimator is more robust than histogram and kernel based approaches, for example densities like the Cauchy distribution (which lack finite moments) can be inferred without the
6063:
With such a small sample size, if one wants at least 95% confidence, one is reduced to saying that the median is between the minimum and the maximum of the 6 observations with probability 31/32 or approximately 97%. Size 6 is, in fact, the smallest sample size such that the interval determined by the
5809:
As an example, consider a random sample of size 6. In that case, the sample median is usually defined as the midpoint of the interval delimited by the 3rd and 4th order statistics. However, we know from the preceding discussion that the probability that this interval actually contains the population
9771:
th smallest (or largest) element of a list is called the selection problem and is solved by a selection algorithm. Although this problem is difficult for very large lists, sophisticated selection algorithms have been created that can solve this problem in time proportional to the number of elements
5908:
of the population median, what this example illustrates is that it is not a particularly good one in absolute terms. In this particular case, a better confidence interval for the median is the one delimited by the 2nd and 5th order statistics, which contains the population median with probability
9146:{\displaystyle {\begin{aligned}P(X_{(k)}<x)&=P({\text{there are at least }}k{\text{ observations less than }}x),\\&=P({\text{there are at most }}n-k{\text{ observations greater than or equal to }}x),\\&=\sum _{j=0}^{n-k}{n \choose j}(p_{2}+p_{3})^{j}(p_{1})^{n-j}.\end{aligned}}}
8830:{\displaystyle {\begin{aligned}P(X_{(k)}\leq x)&=P({\text{there are at least }}k{\text{ observations less than or equal to }}x),\\&=P({\text{there are at most }}n-k{\text{ observations greater than }}x),\\&=\sum _{j=0}^{n-k}{n \choose j}p_{3}^{j}(p_{1}+p_{2})^{n-j}.\end{aligned}}}
4312:{\displaystyle \operatorname {Var} (U_{(k)}-U_{(j)})=\operatorname {Var} (U_{(k)})+\operatorname {Var} (U_{(j)})-2\cdot \operatorname {Cov} (U_{(k)},U_{(j)})={\frac {k(n-k+1)}{(n+1)^{2}(n+2)}}+{\frac {j(n-j+1)}{(n+1)^{2}(n+2)}}-2\cdot \operatorname {Cov} (U_{(k)},U_{(j)})}
7225:
2940:
4746:
5529:
8548:
5722:
1690:
1530:
6359:
3935:
8050:
4445:
3356:
6182:
1379:
8146:
5189:
6524:
2638:
625:
6640:
3799:
2178:
1167:
2266:
276:
5899:
10242:
M. Cardone, A. Dytso and C. Rush, "Entropic
Central Limit Theorem for Order Statistics," in IEEE Transactions on Information Theory, vol. 69, no. 4, pp. 2193-2205, April 2023, doi: 10.1109/TIT.2022.3219344.
4519:
6058:
501:
391:
6905:
7588:
5784:
7527:
9200:
8899:
8591:
3425:
6979:
2702:
1724:
family. We also give a simple method to derive the joint distribution of any number of order statistics, and finally translate these results to arbitrary continuous distributions using the
7351:
7429:
8264:
1788:
7635:
7043:
4630:
5197:
4869:
1993:
4589:
6799:
1921:
3641:
1875:
7675:
8886:
4972:
3804:
3693:
3603:
8199:. This is because the first moment of the order statistic always exists if the expected value of the underlying distribution does, but the converse is not necessarily true.
8578:
8352:
3499:
3469:
7868:
7823:
396:
where, following a common convention, we use upper-case letters to refer to random variables, and lower-case letters (as above) to refer to their actual observed values.
8360:
8182:
7901:
7788:
7467:
4914:
7928:
5563:
4322:
2982:
2373:
1538:
797:
705:
3198:
3157:
3116:
3075:
2499:
2458:
989:
9187:
7015:
5555:
2302:
2029:
1390:
758:
7705:
7759:
7732:
7275:
6736:
6709:
3034:
2417:
1819:
8325:
8293:
3525:
6205:
3548:
7948:
7378:
7248:
7035:
6399:
An interesting observation can be made in the case where the distribution is symmetric, and the population median equals the population mean. In this case, the
6392:
representation which provides information about the errorbounds. The convergence to normal distribution also holds in a stronger sense, such as convergence in
6684:
Moments of the distribution for the first order statistic can be used to develop a non-parametric density estimator. Suppose, we want to estimate the density
3698:
799:, and the sample median is some function of the two (usually the average) and hence not an order statistic. Similar remarks apply to all sample quantiles.
9772:
in the list, even if the list is totally unordered. If the data is stored in certain specialized data structures, this time can be brought down to O(log
7957:
3217:
6090:
1178:
8055:
4991:
6437:
2511:
11779:
516:
6535:
2037:
12284:
1001:
2197:
145:
12434:
3203:
One reasons in an entirely analogous way to derive the higher-order joint distributions. Perhaps surprisingly, the joint density of the
12058:
10699:
10171:
Hlynka, M.; Brill, P. H.; Horn, W. (2010). "A method for obtaining
Laplace transforms of order statistics of Erlang random variables".
3431:
that the maximum expected number of uniform U(0,1] random variables one can choose from a sample of size n with a sum up not exceeding
5816:
11832:
3365:! different permutations of the sample corresponding to the same sequence of order statistics. This is related to the fact that 1/
12271:
897:
4450:
5915:
427:
320:
6804:
3553:
Using the above formulas, one can derive the distribution of the range of the order statistics, that is the distribution of
10694:
10394:
7535:
5727:
131:
For example, suppose that four numbers are observed or recorded, resulting in a sample of size 4. If the sample values are
7472:
11298:
10446:
3372:
2935:{\displaystyle f_{U_{(i)},U_{(j)}}(u,v)=n!{u^{i-1} \over (i-1)!}{(v-u)^{j-i-1} \over (j-i-1)!}{(1-v)^{n-j} \over (n-j)!}}
932:
112:
6910:
3427:. It is also related with another particularity of order statistics of uniform random variables: It follows from the
12708:
12081:
11973:
10318:
10207:
10118:
10047:
10017:
9990:
9946:
9924:
1924:
1709:
120:
9917:
12686:
12259:
12133:
7280:
1725:
116:
17:
3361:
One way to understand this is that the unordered sample does have constant density equal to 1, and that there are
641:
The sample median may or may not be an order statistic, since there is a single middle value only when the number
12317:
11978:
11723:
11094:
10684:
9817:
7383:
6393:
7220:{\displaystyle E(Y_{(1)})={\frac {1}{(N+1)g(0)}}+{\frac {1}{(N+1)(N+2)}}\int _{0}^{1}Q''(z)\delta _{N+1}(z)\,dz}
4741:{\displaystyle X_{(i)}{\stackrel {d}{=}}{\frac {1}{\lambda }}\left(\sum _{j=1}^{i}{\frac {Z_{j}}{n-j+1}}\right)}
12368:
11580:
11387:
11276:
11234:
10063:
Jones, M. C. (2009), "Kumaraswamy's distribution: A beta-type distribution with some tractability advantages",
8210:
5524:{\displaystyle f_{X_{(j)},X_{(k)}}(x,y)={\frac {n!}{(j-1)!(k-j-1)!(n-k)!}}^{j-1}^{k-1-j}^{n-k}f_{X}(x)f_{X}(y)}
4762:
are iid standard exponential random variables (i.e. with rate parameter 1). This result was first published by
2671:
1734:
921:
11308:
7593:
12611:
11570:
10473:
4806:
1930:
12162:
12111:
12096:
12086:
11955:
11827:
11794:
11620:
11575:
11405:
936:
34:
4785:
4532:
12713:
12674:
12506:
12307:
12231:
11532:
11286:
10955:
10419:
6741:
1880:
3608:
1824:
12391:
12363:
12358:
12106:
11865:
11771:
11751:
11659:
11370:
11188:
10671:
10543:
10142:
9891:
9856:
7640:
12123:
11891:
11612:
11537:
11466:
11395:
11315:
11303:
11173:
11161:
11154:
10862:
10583:
10367:
8843:
8296:
8191:
4925:
3646:
3556:
847:
631:
74:
9825:
for the order statistics of independent but not necessarily identically distributed random variables
12606:
12373:
12236:
11921:
11886:
11850:
11635:
11077:
10986:
10945:
10857:
10548:
10387:
9911:
9812:
8556:
8543:{\displaystyle p_{1}=P(X<x)=F(x)-f(x),\ p_{2}=P(X=x)=f(x),{\text{ and }}p_{3}=P(X>x)=1-F(x).}
8330:
6653:
4977:
to derive the following probability density functions for the order statistics of a sample of size
4596:
3474:
3434:
2502:
1172:
the corresponding probability density function may be derived from this result, and is found to be
917:
78:
42:
7834:
7796:
5717:{\displaystyle f_{X_{(1)},\ldots ,X_{(n)}}(x_{1},\ldots ,x_{n})=n!f_{X}(x_{1})\cdots f_{X}(x_{n})}
1685:{\displaystyle F_{X_{(1)}}(x)=\operatorname {Prob} (\min\{\,X_{1},\ldots ,X_{n}\,\}\leq x)=1-^{n}}
12515:
12128:
12068:
12005:
11643:
11627:
11365:
11227:
11217:
11067:
10981:
8158:
7876:
7764:
7434:
6411:
instead. This asymptotic analysis suggests that the mean outperforms the median in cases of low
4877:
1525:{\displaystyle F_{X_{(n)}}(x)=\operatorname {Prob} (\max\{\,X_{1},\ldots ,X_{n}\,\}\leq x)=^{n}}
12553:
12483:
12276:
12213:
11968:
11855:
10852:
10749:
10656:
10535:
10434:
9928:
9871:
9839:
8266:
are i.i.d. random variables from a discrete distribution with cumulative distribution function
8196:
7906:
2948:
2339:
763:
671:
10007:
3162:
3121:
3080:
3039:
2463:
2422:
958:
943:. The peculiarities of the analysis of distributions assigning mass to points (in particular,
510:
is the difference between the maximum and minimum. It is a function of the order statistics:
12718:
12578:
12520:
12463:
12289:
12182:
12091:
11817:
11701:
11560:
11552:
11442:
11434:
11249:
11145:
11123:
11082:
11047:
11014:
10960:
10935:
10890:
10829:
10789:
10591:
10414:
10037:
9822:
9159:
6987:
6672:
are asymptotically normally distributed by the CLT, our results follow by application of the
6404:
5806:
The simplest case to consider is how well the sample median estimates the population median.
5534:
2657:
2274:
2001:
1717:
944:
925:
730:
7680:
12501:
12076:
12025:
12001:
11963:
11881:
11860:
11812:
11691:
11669:
11638:
11547:
11424:
11375:
11293:
11266:
11222:
11178:
10940:
10716:
10596:
9828:
7737:
7710:
7354:
7253:
6714:
6687:
6416:
6354:{\displaystyle X_{(\lceil np\rceil )}\sim AN\left(F^{-1}(p),{\frac {p(1-p)}{n^{2}}}\right)}
3007:
2390:
1797:
714:
648:
70:
8301:
8269:
8:
12648:
12573:
12496:
12177:
11941:
11934:
11896:
11804:
11784:
11756:
11489:
11355:
11350:
11340:
11332:
11150:
11111:
11001:
10991:
10900:
10679:
10635:
10553:
10478:
10380:
10198:
9844:
9758:
6385:
6081:
6064:
minimum and the maximum is at least a 95% confidence interval for the population median.
4800:
4779:
3504:
940:
893:
635:
3930:{\displaystyle \operatorname {Cov} (U_{(k)},U_{(j)})={\frac {j(n-k+1)}{(n+1)^{2}(n+2)}}}
3530:
12662:
12473:
12327:
12223:
12172:
12048:
11945:
11929:
11906:
11683:
11417:
11400:
11360:
11271:
11166:
11128:
11099:
11059:
11019:
10965:
10882:
10568:
10563:
10283:
10265:
7933:
7363:
7233:
7020:
6415:, and vice versa. For example, the median achieves better confidence intervals for the
4786:
The joint distribution of the order statistics of an absolutely continuous distribution
991:, the order statistics for that sample have cumulative distributions as follows (where
104:
62:
5794:
An interesting question is how well the order statistics perform as estimators of the
12657:
12568:
12538:
12530:
12350:
12341:
12266:
12197:
12053:
12038:
12013:
11901:
11842:
11708:
11696:
11322:
11239:
11183:
11106:
10950:
10872:
10651:
10525:
10348:
10314:
10133:
10114:
10043:
10013:
9986:
9777:
9762:
6389:
6377:
4775:
4763:
2188:
1721:
10351:
10287:
12593:
12548:
12312:
12299:
12192:
12167:
12101:
12033:
11911:
11519:
11412:
11345:
11258:
11205:
11024:
10895:
10689:
10573:
10488:
10455:
10306:
10275:
10216:
10180:
10151:
10106:
10072:
9978:
6369:
30:
10202:
8045:{\displaystyle x_{\ell }:d_{\ell }=\sum _{k=1}^{m_{N}}{\frac {d_{\ell k}}{m_{N}}}}
4440:{\displaystyle \operatorname {Var} (U)={\frac {(k-j)(n-(k-j)+1)}{(n+1)^{2}(n+2)}}}
3351:{\displaystyle f_{U_{(1)},U_{(2)},\ldots ,U_{(n)}}(u_{1},u_{2},\ldots ,u_{n})=n!.}
12510:
12254:
12116:
12043:
11718:
11592:
11565:
11542:
11511:
11138:
11133:
10817:
10468:
10279:
10076:
1384:
Moreover, there are two special cases, which have CDFs that are easy to compute.
12000:
10301:
David, H. A.; Nagaraja, H. N. (2003), "Chapter 3. Expected Values and
Moments",
6177:{\displaystyle U_{(\lceil np\rceil )}\sim AN\left(p,{\frac {p(1-p)}{n}}\right).}
12459:
12454:
10917:
10847:
10493:
9807:
5905:
5904:
Although the sample median is probably among the best distribution-independent
3428:
10221:
10184:
10101:
David, H. A.; Nagaraja, H. N. (2003), "Chapter 2. Basic
Distribution Theory",
3801:
From these formulas we can derive the covariance between two order statistics:
1374:{\displaystyle f_{X_{(r)}}(x)={\frac {n!}{(r-1)!(n-r)!}}f_{X}(x)^{r-1}^{n-r}.}
931:
From now on, we will assume that the random variables under consideration are
12702:
12616:
12583:
12446:
12407:
12218:
12187:
11651:
11605:
11210:
10912:
10739:
10503:
10498:
10253:
8141:{\displaystyle x_{\ell }:{\hat {f}}_{\ell }={\frac {1}{2(1+s_{N})d_{\ell }}}}
5184:{\displaystyle f_{X_{(k)}}(x)={\frac {n!}{(k-1)!(n-k)!}}^{k-1}^{n-k}f_{X}(x)}
1791:
1713:
108:
93:
7357:
technique becomes the basis for the following density estimation algorithm,
6519:{\displaystyle B(k,n+1-k)\ {\stackrel {\mathrm {d} }{=}}\ {\frac {X}{X+Y}},}
4524:
12558:
12491:
12468:
12383:
11713:
11009:
10907:
10842:
10784:
10769:
10706:
10661:
10310:
10110:
9776:). In many applications all order statistics are required, in which case a
6673:
2336:. The probability that more than one is in this latter interval is already
507:
2658:
The joint distribution of the order statistics of the uniform distribution
2633:{\displaystyle {n! \over (k-1)!(n-k)!}u^{k-1}\cdot du\cdot (1-u-du)^{n-k}}
12601:
12563:
12246:
12147:
12009:
11822:
11789:
11281:
11198:
11193:
10837:
10794:
10774:
10754:
10744:
10513:
10336:
9833:
6400:
620:{\displaystyle {\rm {Range}}\{\,X_{1},\ldots ,X_{n}\,\}=X_{(n)}-X_{(1)}.}
6635:{\displaystyle X=\sum _{i=1}^{k}Z_{i},\quad Y=\sum _{i=k+1}^{n+1}Z_{i},}
3794:{\displaystyle U_{(k)}-U_{(j)}\sim \operatorname {Beta} (k-j,n-(k-j)+1)}
2173:{\displaystyle f_{U_{(k)}}(u)={n! \over (k-1)!(n-k)!}u^{k-1}(1-u)^{n-k}}
11447:
10927:
10627:
10558:
10508:
10483:
10403:
10340:
10156:
10137:
9982:
9866:
6388:
in his seminal paper in 1946. Further research led in the 1960s to the
4769:
1703:
1162:{\displaystyle F_{X_{(r)}}(x)=\sum _{j=r}^{n}{\binom {n}{j}}^{j}^{n-j}}
950:
50:
2261:{\displaystyle U_{(k)}\sim \operatorname {Beta} (k,n+1\mathbf {-} k).}
271:{\displaystyle x_{(1)}=3,\ \ x_{(2)}=6,\ \ x_{(3)}=7,\ \ x_{(4)}=9,\,}
119:
is used to reduce the analysis to the case of order statistics of the
92:
value of a sample, and (with some qualifications discussed below) the
11600:
11452:
11072:
10867:
10779:
10764:
10759:
10724:
10356:
8187:
11116:
10734:
10611:
10606:
10601:
10081:
As is well known, the beta distribution is the distribution of the
9876:
9861:
9802:
6412:
5795:
916:
can arise by sampling from more than one population. Then they are
900:. This is the case treated below. In general, the random variables
97:
10270:
6407:, is also asymptotically normally distributed, but with variance Ï
5789:
12621:
12322:
6679:
418:
311:
89:
85:
8186:
In contrast to the bandwidth/length based tuning parameters for
5894:{\displaystyle {6 \choose 3}(1/2)^{6}={5 \over 16}\approx 31\%.}
1698:
1695:
Which can be derived by careful consideration of probabilities.
12543:
11524:
11498:
11478:
10729:
10520:
9881:
9797:
6384:. One of the first people to mention and prove this result was
10372:
634:
that is simply related to the order statistics is the sample
935:
and, where convenient, we will also assume that they have a
10463:
9886:
955:
For a random sample as above, with cumulative distribution
73:, order statistics are among the most fundamental tools in
10305:, Wiley Series in Probability and Statistics, p. 34,
7250:
is the quantile function associated with the distribution
4514:{\displaystyle U\sim \operatorname {Beta} (k-j,n-(k-j)+1)}
846:
are also random variables, defined by sorting the values (
10105:, Wiley Series in Probability and Statistics, p. 9,
6053:{\displaystyle \left(1/2)^{6}={25 \over 32}\approx 78\%.}
4525:
Order statistics sampled from an exponential distribution
1708:
In this section we show that the order statistics of the
920:, but not necessarily identically distributed, and their
10346:
8354:
order statistics, three values are first needed, namely
1998:
The probability density function of the order statistic
496:{\displaystyle X_{(n)}=\max\{\,X_{1},\ldots ,X_{n}\,\}.}
84:
Important special cases of the order statistics are the
9189:
is just the difference of these values, that is to say
2375:, so we have to calculate the probability that exactly
2320: â 1 elements of the sample are smaller than
707:
and so is an order statistic. On the other hand, when
386:{\displaystyle X_{(1)}=\min\{\,X_{1},\ldots ,X_{n}\,\}}
6900:{\displaystyle g_{Y}(y)=f_{X}(y+x^{*})+f_{X}(x^{*}-y)}
4521:, which is the actual distribution of the difference.
3605:, i.e. maximum minus the minimum. More generally, for
10256:(2017). "Minimum local distance density estimation".
9198:
9162:
8897:
8846:
8589:
8559:
8363:
8333:
8304:
8272:
8213:
8161:
8058:
7960:
7936:
7909:
7879:
7837:
7799:
7767:
7740:
7713:
7683:
7643:
7596:
7583:{\displaystyle m_{N}=\operatorname {round} (N^{1-a})}
7538:
7475:
7437:
7386:
7366:
7283:
7256:
7236:
7046:
7023:
6990:
6913:
6807:
6744:
6717:
6690:
6538:
6440:
6208:
6093:
5918:
5819:
5779:{\displaystyle x_{1}\leq x_{2}\leq \dots \leq x_{n}.}
5730:
5566:
5537:
5200:
4994:
4928:
4880:
4809:
4633:
4535:
4453:
4325:
3943:
3807:
3701:
3649:
3611:
3559:
3533:
3507:
3477:
3437:
3375:
3220:
3165:
3124:
3083:
3042:
3010:
2951:
2705:
2514:
2466:
2425:
2393:
2342:
2277:
2200:
2040:
2004:
1933:
1883:
1827:
1800:
1737:
1541:
1393:
1181:
1004:
961:
766:
733:
674:
519:
430:
323:
148:
12285:
Autoregressive conditional heteroskedasticity (ARCH)
7522:{\displaystyle \{{\hat {f}}_{\ell }\}_{\ell =1}^{M}}
4770:
Order statistics sampled from an Erlang distribution
2187:
th order statistic of the uniform distribution is a
1704:
Order statistics sampled from a uniform distribution
951:
Cumulative distribution function of order statistics
7954:9: Compute the subset average of distances to
3420:{\displaystyle 0<u_{1}<\cdots <u_{n}<1}
11747:
10251:
9741:
9181:
9145:
8880:
8829:
8572:
8542:
8346:
8319:
8287:
8258:
8202:
8176:
8140:
8044:
7942:
7922:
7895:
7862:
7817:
7782:
7753:
7726:
7699:
7669:
7629:
7582:
7521:
7461:
7423:
7372:
7345:
7269:
7242:
7219:
7029:
7009:
6974:{\displaystyle f_{X}(x^{*})={\frac {g_{Y}(0)}{2}}}
6973:
6899:
6793:
6730:
6703:
6634:
6518:
6353:
6176:
6052:
5893:
5778:
5716:
5549:
5523:
5183:
4966:
4908:
4863:
4740:
4583:
4513:
4439:
4311:
3929:
3793:
3687:
3635:
3597:
3542:
3519:
3493:
3463:
3419:
3350:
3192:
3151:
3110:
3069:
3028:
2976:
2934:
2632:
2493:
2452:
2411:
2367:
2296:
2260:
2172:
2023:
1987:
1915:
1869:
1813:
1782:
1684:
1524:
1373:
1161:
983:
791:
752:
699:
619:
495:
385:
270:
10258:Communications in Statistics - Theory and Methods
10085:'th order statistic from a random sample of size
9559:
9546:
9362:
9349:
9065:
9052:
9000: observations greater than or equal to
8757:
8744:
5990:
5977:
5965:
5952:
5940:
5927:
5836:
5823:
2271:The proof of these statements is as follows. For
1077:
1064:
12700:
6984:The expected value of the first order statistic
1586:
1438:
450:
343:
11833:Multivariate adaptive regression splines (MARS)
10170:
10012:(2nd ed.). Cengage Learning. p. 229.
9850:
8580:order statistic can be computed by noting that
7529:estimated density at the points of evaluation.
7431:points of density evaluation. Tuning parameter
5790:Application: confidence intervals for quantiles
9977:. Wiley Series in Probability and Statistics.
8648: observations less than or equal to
6680:Application: Non-parametric density estimation
5801:
1927:. Note that the order statistics also satisfy
1794:drawn from a continuous distribution with cdf
10388:
10300:
10100:
10005:
9972:
9752:
7346:{\displaystyle \delta _{N}(z)=(N+1)(1-z)^{N}}
6801:, which are i.i.d with distribution function
1699:Probability distributions of order statistics
37:of the order statistics for a sample of size
8553:The cumulative distribution function of the
7499:
7476:
7401:
7387:
6226:
6217:
6111:
6102:
3501:, which is thus invariant on the set of all
1623:
1589:
1475:
1441:
573:
539:
487:
453:
380:
346:
9156:Note that the probability mass function of
8195:need for specialized modifications such as
7424:{\displaystyle \{x_{\ell }\}_{\ell =1}^{M}}
6199:), a similar asymptotic normality applies:
4778:of order statistics may be sampled from an
2945:which is (up to terms of higher order than
10433:
10395:
10381:
6652:being independent identically distributed
1877:we obtain the corresponding random sample
27:Kth smallest value in a statistical sample
11046:
10269:
10220:
10203:"On Some Useful "Inefficient" Statistics"
10197:
10155:
10089:from the uniform distribution (on (0,1)).
9947:Learn how and when to remove this message
9836:â linear combinations of order statistics
8259:{\displaystyle X_{1},X_{2},\ldots ,X_{n}}
8052:10: Compute the density estimate at
7210:
4957:
4854:
2964:
1783:{\displaystyle X_{1},X_{2},\ldots ,X_{n}}
1622:
1592:
1474:
1444:
802:
572:
542:
486:
456:
379:
349:
267:
10191:
10031:
10029:
9910:This article includes a list of general
7761:observations each. 4: Create a vector
7630:{\displaystyle s_{N}={\frac {N}{m_{N}}}}
126:
29:
10006:Casella, George; Berger, Roger (2002).
1731:We assume throughout this section that
898:independent and identically distributed
14:
12701:
12359:KaplanâMeier estimator (product limit)
10035:
9973:David, H. A.; Nagaraja, H. N. (2003).
7790:to hold the density evaluations. 5:
7353:. This equation in combination with a
6191:with a continuous non-zero density at
4864:{\displaystyle dF_{X}(x)=f_{X}(x)\,dx}
3004:sample elements fall in the intervals
1988:{\displaystyle U_{(i)}=F_{X}(X_{(i)})}
291:enclosed in parentheses indicates the
139:the order statistics would be denoted
12432:
11999:
11746:
11045:
10815:
10432:
10376:
10347:
10132:
10062:
10026:
9780:can be used and the time taken is O(
8692: observations greater than
7873:7: Find the nearest distance
6419:, while the mean performs better for
6067:
3937:The formula follows from noting that
12669:
12369:Accelerated failure time (AFT) model
10173:Statistics & Probability Letters
9966:
9896:
6656:random variables with rate 1. Since
4584:{\displaystyle X_{1},X_{2},..,X_{n}}
2501:respectively. This equals (refer to
12681:
11964:Analysis of variance (ANOVA, anova)
10816:
10138:"On the theory of order statistics"
8327:. To find the probabilities of the
6794:{\displaystyle Y_{i}=|X_{i}-x^{*}|}
4871:, and we can use the substitutions
2387:observations fall in the intervals
2324:, and that at least one is between
1916:{\displaystyle U_{1},\ldots ,U_{n}}
24:
12059:CochranâMantelâHaenszel statistics
10685:Pearson product-moment correlation
9916:it lacks sufficient corresponding
9550:
9353:
9056:
8956: observations less than
8748:
6484:
6080:sample quantile is asymptotically
6044:
5981:
5956:
5931:
5885:
5827:
3636:{\displaystyle n\geq k>j\geq 1}
2672:joint probability density function
1870:{\displaystyle U_{i}=F_{X}(X_{i})}
1068:
995:specifies which order statistic):
534:
531:
528:
525:
522:
299:th order statistic of the sample.
25:
12730:
10330:
10208:Annals of Mathematical Statistics
7670:{\displaystyle s_{N}\times m_{N}}
6394:relative entropy or KL divergence
6072:For the uniform distribution, as
3207:order statistics turns out to be
2646:The mean of this distribution is
727:and there are two middle values,
630:A similar important statistic in
69:th-smallest value. Together with
12680:
12668:
12656:
12643:
12642:
12433:
10252:Garg, Vikram V.; Tenorio, Luis;
9901:
6738:. Consider the random variables
5798:of the underlying distribution.
2245:
399:Similarly, for a sample of size
117:cumulative distribution function
12318:Least-squares spectral analysis
10294:
10245:
8881:{\displaystyle P(X_{(k)}<x)}
8203:Dealing with discrete variables
6579:
6423:that are normally distributed.
4981:drawn from the distribution of
4967:{\displaystyle du=f_{X}(x)\,dx}
3688:{\displaystyle U_{(k)}-U_{(j)}}
3598:{\displaystyle U_{(n)}-U_{(1)}}
2316:, it is necessary that exactly
107:to analyze order statistics of
11299:Mean-unbiased minimum-variance
10402:
10236:
10164:
10126:
10094:
10056:
9999:
9712:
9708:
9702:
9693:
9687:
9681:
9672:
9668:
9662:
9653:
9647:
9635:
9617:
9613:
9607:
9601:
9592:
9588:
9582:
9570:
9483:
9469:
9460:
9433:
9415:
9388:
9303:
9292:
9286:
9278:
9269:
9258:
9252:
9244:
9231:
9220:
9214:
9206:
9174:
9168:
9121:
9107:
9098:
9071:
9006:
8981:
8962:
8943:
8930:
8919:
8913:
8905:
8875:
8864:
8858:
8850:
8805:
8778:
8698:
8673:
8654:
8635:
8622:
8611:
8605:
8597:
8534:
8528:
8513:
8501:
8474:
8468:
8459:
8447:
8422:
8416:
8407:
8401:
8392:
8380:
8314:
8308:
8282:
8276:
8168:
8122:
8103:
8079:
7847:
7809:
7774:
7577:
7558:
7486:
7456:
7444:
7334:
7321:
7318:
7306:
7300:
7294:
7207:
7201:
7182:
7176:
7147:
7135:
7132:
7120:
7105:
7099:
7093:
7081:
7069:
7064:
7058:
7050:
7002:
6996:
6962:
6956:
6937:
6924:
6894:
6875:
6859:
6840:
6824:
6818:
6787:
6759:
6468:
6444:
6334:
6330:
6327:
6321:
6305:
6299:
6291:
6279:
6267:
6261:
6229:
6214:
6157:
6145:
6114:
6099:
6084:, since it is approximated by
6016:
6001:
5857:
5842:
5711:
5698:
5682:
5669:
5647:
5615:
5608:
5602:
5583:
5577:
5518:
5512:
5499:
5493:
5468:
5464:
5458:
5439:
5418:
5414:
5408:
5392:
5386:
5373:
5358:
5354:
5348:
5335:
5326:
5314:
5308:
5290:
5284:
5272:
5255:
5243:
5236:
5230:
5217:
5211:
5178:
5172:
5147:
5143:
5137:
5118:
5103:
5099:
5093:
5080:
5071:
5059:
5053:
5041:
5024:
5018:
5011:
5005:
4954:
4948:
4903:
4897:
4851:
4845:
4829:
4823:
4645:
4639:
4508:
4499:
4487:
4466:
4431:
4419:
4410:
4397:
4392:
4383:
4371:
4362:
4359:
4347:
4338:
4332:
4306:
4301:
4295:
4282:
4276:
4268:
4247:
4235:
4226:
4213:
4208:
4190:
4175:
4163:
4154:
4141:
4136:
4118:
4106:
4101:
4095:
4082:
4076:
4068:
4050:
4045:
4039:
4031:
4019:
4014:
4008:
4000:
3988:
3983:
3977:
3964:
3958:
3950:
3921:
3909:
3900:
3887:
3882:
3864:
3852:
3847:
3841:
3828:
3822:
3814:
3788:
3779:
3767:
3746:
3732:
3726:
3713:
3707:
3695:also has a beta distribution:
3680:
3674:
3661:
3655:
3590:
3584:
3571:
3565:
3369:! is the volume of the region
3333:
3288:
3281:
3275:
3256:
3250:
3237:
3231:
3187:
3166:
3146:
3125:
3105:
3084:
3064:
3043:
3023:
3011:
2971:
2955:
2923:
2911:
2894:
2881:
2869:
2851:
2828:
2815:
2803:
2791:
2760:
2748:
2741:
2735:
2722:
2716:
2615:
2593:
2556:
2544:
2538:
2526:
2488:
2467:
2447:
2426:
2406:
2394:
2362:
2346:
2289:
2283:
2252:
2226:
2212:
2206:
2155:
2142:
2117:
2105:
2099:
2087:
2070:
2064:
2057:
2051:
2016:
2010:
1982:
1977:
1971:
1963:
1945:
1939:
1864:
1851:
1673:
1669:
1663:
1644:
1632:
1583:
1571:
1565:
1558:
1552:
1513:
1509:
1503:
1490:
1484:
1435:
1423:
1417:
1410:
1404:
1353:
1349:
1343:
1324:
1309:
1305:
1299:
1286:
1283:
1277:
1258:
1246:
1240:
1228:
1211:
1205:
1198:
1192:
1144:
1140:
1134:
1115:
1106:
1102:
1096:
1083:
1034:
1028:
1021:
1015:
978:
972:
922:joint probability distribution
784:
772:
745:
739:
692:
680:
609:
603:
590:
584:
442:
436:
335:
329:
253:
247:
222:
216:
191:
185:
160:
154:
13:
1:
12612:Geographic information system
11828:Simultaneous equations models
9959:
9767:The problem of computing the
8573:{\displaystyle k^{\text{th}}}
8347:{\displaystyle k^{\text{th}}}
4803:, it has a density such that
4782:via a path counting method .
3494:{\displaystyle {\sqrt {2sn}}}
3464:{\displaystyle 0<s<n/2}
35:Probability density functions
11795:Coefficient of determination
11406:Uniformly most powerful test
10280:10.1080/03610926.2014.988260
10077:10.1016/j.stamet.2008.04.001
9851:Examples of order statistics
7863:{\displaystyle k=1\to m_{N}}
7818:{\displaystyle \ell =1\to M}
2674:of the two order statistics
947:) are discussed at the end.
937:probability density function
668:, then the sample median is
7:
12364:Proportional hazards models
12308:Spectral density estimation
12290:Vector autoregression (VAR)
11724:Maximum posterior estimator
10956:Randomized controlled trial
9818:FisherâTippett distribution
9791:
7037:total observations yields,
6187:For a general distribution
5802:A small-sample-size example
2992: â 1 â
807:Given any random variables
10:
12735:
12124:Multivariate distributions
10544:Average absolute deviation
10143:Acta Mathematica Hungarica
9892:Sample mean and covariance
9857:Sample maximum and minimum
9756:
9753:Computing order statistics
8177:{\displaystyle {\hat {f}}}
7896:{\displaystyle d_{\ell k}}
7783:{\displaystyle {\hat {f}}}
7462:{\displaystyle a\in (0,1)}
4909:{\displaystyle u=F_{X}(x)}
869:When the random variables
12638:
12592:
12529:
12482:
12445:
12441:
12428:
12400:
12382:
12349:
12340:
12298:
12245:
12206:
12155:
12146:
12112:Structural equation model
12067:
12024:
12020:
11995:
11954:
11920:
11874:
11841:
11803:
11770:
11766:
11742:
11682:
11591:
11510:
11474:
11465:
11448:Score/Lagrange multiplier
11433:
11386:
11331:
11257:
11248:
11058:
11054:
11041:
11000:
10974:
10926:
10881:
10863:Sample size determination
10828:
10824:
10811:
10715:
10670:
10644:
10626:
10582:
10534:
10454:
10445:
10441:
10428:
10410:
10185:10.1016/j.spl.2009.09.006
10036:Gentle, James E. (2009),
8297:probability mass function
7923:{\displaystyle x_{\ell }}
7469:(usually 1/3). Output:
2977:{\displaystyle O(du\,dv)}
2368:{\displaystyle O(du^{2})}
939:(PDF), that is, they are
792:{\displaystyle X_{(m+1)}}
700:{\displaystyle X_{(m+1)}}
632:exploratory data analysis
75:non-parametric statistics
45:with unit scale parameter
12709:Nonparametric statistics
12607:Environmental statistics
12129:Elliptical distributions
11922:Generalized linear model
11851:Simple linear regression
11621:HodgesâLehmann estimator
11078:Probability distribution
10987:Stochastic approximation
10549:Coefficient of variation
10368:Dynamic Order Statistics
10343:. Retrieved Feb 02, 2005
10042:, Springer, p. 63,
10039:Computational Statistics
9813:Concomitant (statistics)
8948:there are at least
8640:there are at least
6426:
4597:exponential distribution
4591:a random sample of size
4319:and comparing that with
3193:{\displaystyle (v+dv,1)}
3152:{\displaystyle (v,v+dv)}
3111:{\displaystyle (u+du,v)}
3070:{\displaystyle (u,u+du)}
2643:and the result follows.
2503:multinomial distribution
2494:{\displaystyle (u+du,1)}
2453:{\displaystyle (u,u+du)}
984:{\displaystyle F_{X}(x)}
830:, the order statistics X
314:of the sample, that is,
308:smallest order statistic
43:exponential distribution
12267:Cross-correlation (XCF)
11875:Non-standard predictors
11309:LehmannâScheffĂ© theorem
10982:Adaptive clinical trial
10222:10.1214/aoms/1177730881
10065:Statistical Methodology
9931:more precise citations.
9182:{\displaystyle X_{(k)}}
8986:there are at most
8678:there are at most
7010:{\displaystyle Y_{(1)}}
6076:tends to infinity, the
5550:{\displaystyle x\leq y}
4622:each have distribution
4603:, the order statistics
2984:) the probability that
2297:{\displaystyle U_{(k)}}
2024:{\displaystyle U_{(k)}}
753:{\displaystyle X_{(m)}}
415:largest order statistic
413:th order statistic (or
113:continuous distribution
41: = 5 from an
12663:Mathematics portal
12484:Engineering statistics
12392:NelsonâAalen estimator
11969:Analysis of covariance
11856:Ordinary least squares
11780:Pearson product-moment
11184:Statistical functional
11095:Empirical distribution
10928:Controlled experiments
10657:Frequency distribution
10435:Descriptive statistics
10363:Retrieved Feb 02, 2005
10311:10.1002/0471722162.ch3
10111:10.1002/0471722162.ch2
9840:Rank-size distribution
9743:
9542:
9345:
9183:
9147:
9048:
8882:
8831:
8740:
8574:
8544:
8348:
8321:
8289:
8260:
8178:
8142:
8046:
8014:
7944:
7924:
7897:
7864:
7819:
7784:
7755:
7728:
7701:
7700:{\displaystyle M_{ij}}
7671:
7631:
7584:
7523:
7463:
7425:
7374:
7347:
7271:
7244:
7221:
7031:
7011:
6975:
6901:
6795:
6732:
6705:
6636:
6618:
6565:
6520:
6355:
6178:
6054:
5895:
5780:
5718:
5551:
5525:
5185:
4968:
4910:
4865:
4742:
4701:
4585:
4515:
4441:
4313:
3931:
3795:
3689:
3637:
3599:
3544:
3527:with constant product
3521:
3495:
3465:
3421:
3352:
3194:
3153:
3112:
3071:
3030:
2978:
2936:
2634:
2495:
2454:
2413:
2379: â 1, 1 and
2369:
2298:
2262:
2174:
2025:
1989:
1917:
1871:
1815:
1784:
1718:marginal distributions
1686:
1526:
1375:
1163:
1060:
985:
945:discrete distributions
803:Probabilistic analysis
793:
754:
701:
651:. More precisely, if
621:
497:
387:
272:
46:
12579:Population statistics
12521:System identification
12255:Autocorrelation (ACF)
12183:Exponential smoothing
12097:Discriminant analysis
12092:Canonical correlation
11956:Partition of variance
11818:Regression validation
11662:(JonckheereâTerpstra)
11561:Likelihood-ratio test
11250:Frequentist inference
11162:Locationâscale family
11083:Sampling distribution
11048:Statistical inference
11015:Cross-sectional study
11002:Observational studies
10961:Randomized experiment
10790:Stem-and-leaf display
10592:Central limit theorem
10009:Statistical Inference
9744:
9516:
9319:
9184:
9148:
9022:
8883:
8832:
8714:
8575:
8545:
8349:
8322:
8290:
8261:
8179:
8143:
8047:
7987:
7945:
7925:
7903:to the current point
7898:
7865:
7820:
7785:
7756:
7754:{\displaystyle s_{N}}
7729:
7727:{\displaystyle m_{N}}
7702:
7672:
7632:
7585:
7524:
7464:
7426:
7375:
7348:
7272:
7270:{\displaystyle g_{Y}}
7245:
7222:
7032:
7012:
6976:
6902:
6796:
6733:
6731:{\displaystyle x^{*}}
6706:
6704:{\displaystyle f_{X}}
6637:
6586:
6545:
6521:
6431:It can be shown that
6405:central limit theorem
6356:
6179:
6055:
5896:
5781:
5719:
5552:
5526:
5186:
4969:
4911:
4866:
4801:absolutely continuous
4743:
4681:
4586:
4516:
4442:
4314:
3932:
3796:
3690:
3638:
3600:
3545:
3522:
3496:
3466:
3422:
3353:
3195:
3154:
3113:
3072:
3031:
3029:{\displaystyle (0,u)}
2979:
2937:
2635:
2496:
2455:
2414:
2412:{\displaystyle (0,u)}
2370:
2299:
2263:
2175:
2026:
1990:
1918:
1872:
1816:
1814:{\displaystyle F_{X}}
1785:
1687:
1527:
1376:
1164:
1040:
986:
941:absolutely continuous
866:in increasing order.
794:
755:
702:
622:
498:
388:
304:first order statistic
273:
127:Notation and examples
33:
12502:Probabilistic design
12087:Principal components
11930:Exponential families
11882:Nonlinear regression
11861:General linear model
11823:Mixed effects models
11813:Errors and residuals
11790:Confounding variable
11692:Bayesian probability
11670:Van der Waerden test
11660:Ordered alternative
11425:Multiple comparisons
11304:RaoâBlackwellization
11267:Estimating equations
11223:Statistical distance
10941:Factorial experiment
10474:Arithmetic-Geometric
10199:Mosteller, Frederick
9829:Bernstein polynomial
9196:
9160:
8895:
8844:
8587:
8557:
8361:
8331:
8320:{\displaystyle f(x)}
8302:
8288:{\displaystyle F(x)}
8270:
8211:
8197:IQR based bandwidths
8159:
8056:
7958:
7950:th subset 8:
7934:
7907:
7877:
7835:
7797:
7765:
7738:
7711:
7681:
7641:
7594:
7536:
7473:
7435:
7384:
7364:
7281:
7254:
7234:
7044:
7021:
6988:
6911:
6805:
6742:
6715:
6688:
6536:
6438:
6417:Laplace distribution
6206:
6091:
6082:normally distributed
5916:
5817:
5728:
5564:
5535:
5198:
4992:
4926:
4878:
4807:
4631:
4533:
4451:
4323:
3941:
3805:
3699:
3647:
3609:
3557:
3531:
3505:
3475:
3471:is bounded above by
3435:
3373:
3218:
3163:
3122:
3081:
3040:
3008:
2949:
2703:
2512:
2464:
2423:
2391:
2340:
2275:
2198:
2038:
2002:
1931:
1925:uniform distribution
1881:
1825:
1798:
1735:
1710:uniform distribution
1539:
1391:
1179:
1002:
959:
764:
731:
672:
517:
428:
321:
281:where the subscript
146:
121:uniform distribution
12574:Official statistics
12497:Methods engineering
12178:Seasonal adjustment
11946:Poisson regressions
11866:Bayesian regression
11805:Regression analysis
11785:Partial correlation
11757:Regression analysis
11356:Prediction interval
11351:Likelihood interval
11341:Confidence interval
11333:Interval estimation
11294:Unbiased estimators
11112:Model specification
10992:Up-and-down designs
10680:Partial correlation
10636:Index of dispersion
10554:Interquartile range
9845:Selection algorithm
9759:Selection algorithm
9387:
8777:
7518:
7420:
7360:Input: A sample of
7167:
6386:Frederick Mosteller
4780:Erlang distribution
3520:{\displaystyle s,n}
2988: â 1, 1,
2696:can be shown to be
647:of observations is
636:interquartile range
12714:Summary statistics
12594:Spatial statistics
12474:Medical statistics
12374:First hitting time
12328:Whittle likelihood
11979:Degrees of freedom
11974:Multivariate ANOVA
11907:Heteroscedasticity
11719:Bayesian estimator
11684:Bayesian inference
11533:KolmogorovâSmirnov
11418:Randomization test
11388:Testing hypotheses
11361:Tolerance interval
11272:Maximum likelihood
11167:Exponential family
11100:Density estimation
11060:Statistical theory
11020:Natural experiment
10966:Scientific control
10883:Survey methodology
10569:Standard deviation
10349:Weisstein, Eric W.
10157:10.1007/BF02127580
9983:10.1002/0471722162
9739:
9737:
9373:
9179:
9143:
9141:
8878:
8827:
8825:
8763:
8570:
8540:
8344:
8317:
8285:
8256:
8174:
8138:
8042:
7940:
7920:
7893:
7860:
7815:
7780:
7751:
7724:
7697:
7667:
7627:
7580:
7519:
7498:
7459:
7421:
7400:
7370:
7343:
7267:
7240:
7217:
7153:
7027:
7017:given a sample of
7007:
6971:
6897:
6791:
6728:
6701:
6632:
6516:
6351:
6174:
6068:Large sample sizes
6050:
5891:
5776:
5714:
5547:
5521:
5181:
4964:
4906:
4861:
4738:
4581:
4511:
4437:
4309:
3927:
3791:
3685:
3633:
3595:
3543:{\displaystyle sn}
3540:
3517:
3491:
3461:
3417:
3348:
3190:
3149:
3108:
3067:
3026:
2974:
2932:
2630:
2491:
2450:
2409:
2365:
2294:
2258:
2170:
2021:
1985:
1923:from the standard
1913:
1867:
1811:
1780:
1682:
1522:
1371:
1159:
981:
789:
750:
697:
617:
493:
383:
268:
105:probability theory
63:statistical sample
47:
12696:
12695:
12634:
12633:
12630:
12629:
12569:National accounts
12539:Actuarial science
12531:Social statistics
12424:
12423:
12420:
12419:
12416:
12415:
12351:Survival function
12336:
12335:
12198:Granger causality
12039:Contingency table
12014:Survival analysis
11991:
11990:
11987:
11986:
11843:Linear regression
11738:
11737:
11734:
11733:
11709:Credible interval
11678:
11677:
11461:
11460:
11277:Method of moments
11146:Parametric family
11107:Statistical model
11037:
11036:
11033:
11032:
10951:Random assignment
10873:Statistical power
10807:
10806:
10803:
10802:
10652:Contingency table
10622:
10621:
10489:Generalized/power
10352:"Order Statistic"
9957:
9956:
9949:
9823:BapatâBeg theorem
9778:sorting algorithm
9763:Sampling in order
9557:
9360:
9063:
9001:
8987:
8957:
8949:
8755:
8693:
8679:
8649:
8641:
8567:
8483:
8430:
8341:
8171:
8136:
8082:
8040:
7943:{\displaystyle k}
7777:
7625:
7489:
7373:{\displaystyle N}
7243:{\displaystyle Q}
7151:
7109:
7030:{\displaystyle N}
6969:
6907:. In particular,
6511:
6494:
6489:
6473:
6378:quantile function
6344:
6164:
6036:
5988:
5963:
5938:
5877:
5834:
5333:
5078:
4776:Laplace transform
4731:
4674:
4663:
4435:
4251:
4179:
3925:
3489:
2930:
2876:
2810:
2563:
2191:random variable.
2124:
1722:beta distribution
1720:belonging to the
1265:
1075:
926:BapatâBeg theorem
662:for some integer
241:
238:
210:
207:
179:
176:
16:(Redirected from
12726:
12684:
12683:
12672:
12671:
12661:
12660:
12646:
12645:
12549:Crime statistics
12443:
12442:
12430:
12429:
12347:
12346:
12313:Fourier analysis
12300:Frequency domain
12280:
12227:
12193:Structural break
12153:
12152:
12102:Cluster analysis
12049:Log-linear model
12022:
12021:
11997:
11996:
11938:
11912:Homoscedasticity
11768:
11767:
11744:
11743:
11663:
11655:
11647:
11646:(KruskalâWallis)
11631:
11616:
11571:Cross validation
11556:
11538:AndersonâDarling
11485:
11472:
11471:
11443:Likelihood-ratio
11435:Parametric tests
11413:Permutation test
11396:1- & 2-tails
11287:Minimum distance
11259:Point estimation
11255:
11254:
11206:Optimal decision
11157:
11056:
11055:
11043:
11042:
11025:Quasi-experiment
10975:Adaptive designs
10826:
10825:
10813:
10812:
10690:Rank correlation
10452:
10451:
10443:
10442:
10430:
10429:
10397:
10390:
10383:
10374:
10373:
10362:
10361:
10337:Order statistics
10324:
10323:
10303:Order Statistics
10298:
10292:
10291:
10273:
10249:
10243:
10240:
10234:
10233:
10231:
10229:
10224:
10195:
10189:
10188:
10168:
10162:
10161:
10159:
10130:
10124:
10123:
10103:Order Statistics
10098:
10092:
10091:
10060:
10054:
10052:
10033:
10024:
10023:
10003:
9997:
9996:
9975:Order Statistics
9970:
9952:
9945:
9941:
9938:
9932:
9927:this article by
9918:inline citations
9905:
9904:
9897:
9748:
9746:
9745:
9740:
9738:
9731:
9727:
9726:
9725:
9680:
9679:
9631:
9630:
9600:
9599:
9564:
9563:
9562:
9549:
9541:
9530:
9509:
9502:
9498:
9497:
9496:
9481:
9480:
9468:
9467:
9458:
9457:
9445:
9444:
9429:
9428:
9413:
9412:
9400:
9399:
9386:
9381:
9367:
9366:
9365:
9352:
9344:
9333:
9312:
9296:
9295:
9262:
9261:
9224:
9223:
9188:
9186:
9185:
9180:
9178:
9177:
9152:
9150:
9149:
9144:
9142:
9135:
9134:
9119:
9118:
9106:
9105:
9096:
9095:
9083:
9082:
9070:
9069:
9068:
9055:
9047:
9036:
9015:
9002:
8999:
8988:
8985:
8971:
8958:
8955:
8950:
8947:
8923:
8922:
8887:
8885:
8884:
8879:
8868:
8867:
8836:
8834:
8833:
8828:
8826:
8819:
8818:
8803:
8802:
8790:
8789:
8776:
8771:
8762:
8761:
8760:
8747:
8739:
8728:
8707:
8694:
8691:
8680:
8677:
8663:
8650:
8647:
8642:
8639:
8615:
8614:
8579:
8577:
8576:
8571:
8569:
8568:
8565:
8549:
8547:
8546:
8541:
8494:
8493:
8484:
8481:
8440:
8439:
8428:
8373:
8372:
8353:
8351:
8350:
8345:
8343:
8342:
8339:
8326:
8324:
8323:
8318:
8294:
8292:
8291:
8286:
8265:
8263:
8262:
8257:
8255:
8254:
8236:
8235:
8223:
8222:
8183:
8181:
8180:
8175:
8173:
8172:
8164:
8147:
8145:
8144:
8139:
8137:
8135:
8134:
8133:
8121:
8120:
8095:
8090:
8089:
8084:
8083:
8075:
8068:
8067:
8051:
8049:
8048:
8043:
8041:
8039:
8038:
8029:
8028:
8016:
8013:
8012:
8011:
8001:
7983:
7982:
7970:
7969:
7949:
7947:
7946:
7941:
7929:
7927:
7926:
7921:
7919:
7918:
7902:
7900:
7899:
7894:
7892:
7891:
7869:
7867:
7866:
7861:
7859:
7858:
7824:
7822:
7821:
7816:
7789:
7787:
7786:
7781:
7779:
7778:
7770:
7760:
7758:
7757:
7752:
7750:
7749:
7733:
7731:
7730:
7725:
7723:
7722:
7706:
7704:
7703:
7698:
7696:
7695:
7676:
7674:
7673:
7668:
7666:
7665:
7653:
7652:
7636:
7634:
7633:
7628:
7626:
7624:
7623:
7611:
7606:
7605:
7589:
7587:
7586:
7581:
7576:
7575:
7548:
7547:
7528:
7526:
7525:
7520:
7517:
7512:
7497:
7496:
7491:
7490:
7482:
7468:
7466:
7465:
7460:
7430:
7428:
7427:
7422:
7419:
7414:
7399:
7398:
7379:
7377:
7376:
7371:
7352:
7350:
7349:
7344:
7342:
7341:
7293:
7292:
7276:
7274:
7273:
7268:
7266:
7265:
7249:
7247:
7246:
7241:
7226:
7224:
7223:
7218:
7200:
7199:
7175:
7166:
7161:
7152:
7150:
7115:
7110:
7108:
7076:
7068:
7067:
7036:
7034:
7033:
7028:
7016:
7014:
7013:
7008:
7006:
7005:
6980:
6978:
6977:
6972:
6970:
6965:
6955:
6954:
6944:
6936:
6935:
6923:
6922:
6906:
6904:
6903:
6898:
6887:
6886:
6874:
6873:
6858:
6857:
6839:
6838:
6817:
6816:
6800:
6798:
6797:
6792:
6790:
6785:
6784:
6772:
6771:
6762:
6754:
6753:
6737:
6735:
6734:
6729:
6727:
6726:
6710:
6708:
6707:
6702:
6700:
6699:
6641:
6639:
6638:
6633:
6628:
6627:
6617:
6606:
6575:
6574:
6564:
6559:
6525:
6523:
6522:
6517:
6512:
6510:
6496:
6492:
6491:
6490:
6488:
6487:
6481:
6476:
6471:
6380:associated with
6370:density function
6360:
6358:
6357:
6352:
6350:
6346:
6345:
6343:
6342:
6341:
6320:
6319:
6294:
6274:
6260:
6259:
6233:
6232:
6183:
6181:
6180:
6175:
6170:
6166:
6165:
6160:
6140:
6118:
6117:
6059:
6057:
6056:
6051:
6037:
6029:
6024:
6023:
6011:
6000:
5996:
5995:
5994:
5993:
5980:
5970:
5969:
5968:
5955:
5945:
5944:
5943:
5930:
5900:
5898:
5897:
5892:
5878:
5870:
5865:
5864:
5852:
5841:
5840:
5839:
5826:
5785:
5783:
5782:
5777:
5772:
5771:
5753:
5752:
5740:
5739:
5723:
5721:
5720:
5715:
5710:
5709:
5697:
5696:
5681:
5680:
5668:
5667:
5646:
5645:
5627:
5626:
5614:
5613:
5612:
5611:
5587:
5586:
5556:
5554:
5553:
5548:
5530:
5528:
5527:
5522:
5511:
5510:
5492:
5491:
5482:
5481:
5457:
5456:
5438:
5437:
5407:
5406:
5385:
5384:
5372:
5371:
5347:
5346:
5334:
5332:
5270:
5262:
5242:
5241:
5240:
5239:
5221:
5220:
5190:
5188:
5187:
5182:
5171:
5170:
5161:
5160:
5136:
5135:
5117:
5116:
5092:
5091:
5079:
5077:
5039:
5031:
5017:
5016:
5015:
5014:
4973:
4971:
4970:
4965:
4947:
4946:
4915:
4913:
4912:
4907:
4896:
4895:
4870:
4868:
4867:
4862:
4844:
4843:
4822:
4821:
4747:
4745:
4744:
4739:
4737:
4733:
4732:
4730:
4713:
4712:
4703:
4700:
4695:
4675:
4667:
4665:
4664:
4662:
4657:
4652:
4649:
4648:
4590:
4588:
4587:
4582:
4580:
4579:
4558:
4557:
4545:
4544:
4520:
4518:
4517:
4512:
4446:
4444:
4443:
4438:
4436:
4434:
4418:
4417:
4395:
4345:
4318:
4316:
4315:
4310:
4305:
4304:
4286:
4285:
4252:
4250:
4234:
4233:
4211:
4185:
4180:
4178:
4162:
4161:
4139:
4113:
4105:
4104:
4086:
4085:
4049:
4048:
4018:
4017:
3987:
3986:
3968:
3967:
3936:
3934:
3933:
3928:
3926:
3924:
3908:
3907:
3885:
3859:
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3832:
3831:
3800:
3798:
3797:
3792:
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3735:
3717:
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3694:
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3691:
3686:
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3642:
3640:
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3634:
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3575:
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3549:
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3526:
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3117:
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3076:
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2813:
2811:
2809:
2789:
2788:
2773:
2747:
2746:
2745:
2744:
2726:
2725:
2685: <
2666: <
2639:
2637:
2636:
2631:
2629:
2628:
2580:
2579:
2564:
2562:
2524:
2516:
2500:
2498:
2497:
2492:
2459:
2457:
2456:
2451:
2418:
2416:
2415:
2410:
2374:
2372:
2371:
2366:
2361:
2360:
2303:
2301:
2300:
2295:
2293:
2292:
2267:
2265:
2264:
2259:
2248:
2216:
2215:
2189:beta-distributed
2179:
2177:
2176:
2171:
2169:
2168:
2141:
2140:
2125:
2123:
2085:
2077:
2063:
2062:
2061:
2060:
2030:
2028:
2027:
2022:
2020:
2019:
1994:
1992:
1991:
1986:
1981:
1980:
1962:
1961:
1949:
1948:
1922:
1920:
1919:
1914:
1912:
1911:
1893:
1892:
1876:
1874:
1873:
1868:
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1862:
1850:
1849:
1837:
1836:
1820:
1818:
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1812:
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1789:
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1786:
1781:
1779:
1778:
1760:
1759:
1747:
1746:
1691:
1689:
1688:
1683:
1681:
1680:
1662:
1661:
1621:
1620:
1602:
1601:
1564:
1563:
1562:
1561:
1531:
1529:
1528:
1523:
1521:
1520:
1502:
1501:
1473:
1472:
1454:
1453:
1416:
1415:
1414:
1413:
1380:
1378:
1377:
1372:
1367:
1366:
1342:
1341:
1323:
1322:
1298:
1297:
1276:
1275:
1266:
1264:
1226:
1218:
1204:
1203:
1202:
1201:
1168:
1166:
1165:
1160:
1158:
1157:
1133:
1132:
1114:
1113:
1095:
1094:
1082:
1081:
1080:
1067:
1059:
1054:
1027:
1026:
1025:
1024:
990:
988:
987:
982:
971:
970:
924:is given by the
798:
796:
795:
790:
788:
787:
759:
757:
756:
751:
749:
748:
726:
712:
706:
704:
703:
698:
696:
695:
667:
661:
646:
626:
624:
623:
618:
613:
612:
594:
593:
571:
570:
552:
551:
538:
537:
502:
500:
499:
494:
485:
484:
466:
465:
446:
445:
412:
411:
404:
392:
390:
389:
384:
378:
377:
359:
358:
339:
338:
310:) is always the
298:
297:
290:
288:
277:
275:
274:
269:
257:
256:
239:
236:
226:
225:
208:
205:
195:
194:
177:
174:
164:
163:
98:sample quantiles
65:is equal to its
21:
18:Order statistics
12734:
12733:
12729:
12728:
12727:
12725:
12724:
12723:
12699:
12698:
12697:
12692:
12655:
12626:
12588:
12525:
12511:quality control
12478:
12460:Clinical trials
12437:
12412:
12396:
12384:Hazard function
12378:
12332:
12294:
12278:
12241:
12237:BreuschâGodfrey
12225:
12202:
12142:
12117:Factor analysis
12063:
12044:Graphical model
12016:
11983:
11950:
11936:
11916:
11870:
11837:
11799:
11762:
11761:
11730:
11674:
11661:
11653:
11645:
11629:
11614:
11593:Rank statistics
11587:
11566:Model selection
11554:
11512:Goodness of fit
11506:
11483:
11457:
11429:
11382:
11327:
11316:Median unbiased
11244:
11155:
11088:Order statistic
11050:
11029:
10996:
10970:
10922:
10877:
10820:
10818:Data collection
10799:
10711:
10666:
10640:
10618:
10578:
10530:
10447:Continuous data
10437:
10424:
10406:
10401:
10333:
10328:
10327:
10321:
10299:
10295:
10250:
10246:
10241:
10237:
10227:
10225:
10196:
10192:
10169:
10165:
10131:
10127:
10121:
10099:
10095:
10061:
10057:
10050:
10034:
10027:
10020:
10004:
10000:
9993:
9971:
9967:
9962:
9953:
9942:
9936:
9933:
9923:Please help to
9922:
9906:
9902:
9853:
9794:
9765:
9757:Main articles:
9755:
9736:
9735:
9715:
9711:
9675:
9671:
9620:
9616:
9595:
9591:
9569:
9565:
9558:
9545:
9544:
9543:
9531:
9520:
9507:
9506:
9486:
9482:
9476:
9472:
9463:
9459:
9453:
9449:
9440:
9436:
9418:
9414:
9408:
9404:
9395:
9391:
9382:
9377:
9372:
9368:
9361:
9348:
9347:
9346:
9334:
9323:
9310:
9309:
9285:
9281:
9251:
9247:
9234:
9213:
9209:
9199:
9197:
9194:
9193:
9167:
9163:
9161:
9158:
9157:
9140:
9139:
9124:
9120:
9114:
9110:
9101:
9097:
9091:
9087:
9078:
9074:
9064:
9051:
9050:
9049:
9037:
9026:
9013:
9012:
8998:
8984:
8969:
8968:
8954:
8946:
8933:
8912:
8908:
8898:
8896:
8893:
8892:
8857:
8853:
8845:
8842:
8841:
8824:
8823:
8808:
8804:
8798:
8794:
8785:
8781:
8772:
8767:
8756:
8743:
8742:
8741:
8729:
8718:
8705:
8704:
8690:
8676:
8661:
8660:
8646:
8638:
8625:
8604:
8600:
8590:
8588:
8585:
8584:
8564:
8560:
8558:
8555:
8554:
8489:
8485:
8482: and
8480:
8435:
8431:
8368:
8364:
8362:
8359:
8358:
8338:
8334:
8332:
8329:
8328:
8303:
8300:
8299:
8271:
8268:
8267:
8250:
8246:
8231:
8227:
8218:
8214:
8212:
8209:
8208:
8205:
8184:
8163:
8162:
8160:
8157:
8156:
8129:
8125:
8116:
8112:
8099:
8094:
8085:
8074:
8073:
8072:
8063:
8059:
8057:
8054:
8053:
8034:
8030:
8021:
8017:
8015:
8007:
8003:
8002:
7991:
7978:
7974:
7965:
7961:
7959:
7956:
7955:
7935:
7932:
7931:
7914:
7910:
7908:
7905:
7904:
7884:
7880:
7878:
7875:
7874:
7854:
7850:
7836:
7833:
7832:
7798:
7795:
7794:
7769:
7768:
7766:
7763:
7762:
7745:
7741:
7739:
7736:
7735:
7718:
7714:
7712:
7709:
7708:
7688:
7684:
7682:
7679:
7678:
7661:
7657:
7648:
7644:
7642:
7639:
7638:
7619:
7615:
7610:
7601:
7597:
7595:
7592:
7591:
7565:
7561:
7543:
7539:
7537:
7534:
7533:
7530:
7513:
7502:
7492:
7481:
7480:
7479:
7474:
7471:
7470:
7436:
7433:
7432:
7415:
7404:
7394:
7390:
7385:
7382:
7381:
7365:
7362:
7361:
7337:
7333:
7288:
7284:
7282:
7279:
7278:
7261:
7257:
7255:
7252:
7251:
7235:
7232:
7231:
7189:
7185:
7168:
7162:
7157:
7119:
7114:
7080:
7075:
7057:
7053:
7045:
7042:
7041:
7022:
7019:
7018:
6995:
6991:
6989:
6986:
6985:
6950:
6946:
6945:
6943:
6931:
6927:
6918:
6914:
6912:
6909:
6908:
6882:
6878:
6869:
6865:
6853:
6849:
6834:
6830:
6812:
6808:
6806:
6803:
6802:
6786:
6780:
6776:
6767:
6763:
6758:
6749:
6745:
6743:
6740:
6739:
6722:
6718:
6716:
6713:
6712:
6695:
6691:
6689:
6686:
6685:
6682:
6650:
6623:
6619:
6607:
6590:
6570:
6566:
6560:
6549:
6537:
6534:
6533:
6500:
6495:
6483:
6482:
6477:
6475:
6474:
6439:
6436:
6435:
6429:
6337:
6333:
6312:
6308:
6295:
6275:
6273:
6252:
6248:
6247:
6243:
6213:
6209:
6207:
6204:
6203:
6141:
6139:
6132:
6128:
6098:
6094:
6092:
6089:
6088:
6070:
6028:
6019:
6015:
6007:
5989:
5976:
5975:
5974:
5964:
5951:
5950:
5949:
5939:
5926:
5925:
5924:
5923:
5919:
5917:
5914:
5913:
5906:point estimates
5869:
5860:
5856:
5848:
5835:
5822:
5821:
5820:
5818:
5815:
5814:
5804:
5792:
5767:
5763:
5748:
5744:
5735:
5731:
5729:
5726:
5725:
5705:
5701:
5692:
5688:
5676:
5672:
5663:
5659:
5641:
5637:
5622:
5618:
5601:
5597:
5576:
5572:
5571:
5567:
5565:
5562:
5561:
5536:
5533:
5532:
5506:
5502:
5487:
5483:
5471:
5467:
5452:
5448:
5421:
5417:
5402:
5398:
5380:
5376:
5361:
5357:
5342:
5338:
5271:
5263:
5261:
5229:
5225:
5210:
5206:
5205:
5201:
5199:
5196:
5195:
5166:
5162:
5150:
5146:
5131:
5127:
5106:
5102:
5087:
5083:
5040:
5032:
5030:
5004:
5000:
4999:
4995:
4993:
4990:
4989:
4942:
4938:
4927:
4924:
4923:
4891:
4887:
4879:
4876:
4875:
4839:
4835:
4817:
4813:
4808:
4805:
4804:
4798:
4788:
4772:
4761:
4714:
4708:
4704:
4702:
4696:
4685:
4680:
4676:
4666:
4658:
4653:
4651:
4650:
4638:
4634:
4632:
4629:
4628:
4613:
4599:with parameter
4575:
4571:
4553:
4549:
4540:
4536:
4534:
4531:
4530:
4527:
4452:
4449:
4448:
4413:
4409:
4396:
4346:
4344:
4324:
4321:
4320:
4294:
4290:
4275:
4271:
4229:
4225:
4212:
4186:
4184:
4157:
4153:
4140:
4114:
4112:
4094:
4090:
4075:
4071:
4038:
4034:
4007:
4003:
3976:
3972:
3957:
3953:
3942:
3939:
3938:
3903:
3899:
3886:
3860:
3858:
3840:
3836:
3821:
3817:
3806:
3803:
3802:
3725:
3721:
3706:
3702:
3700:
3697:
3696:
3673:
3669:
3654:
3650:
3648:
3645:
3644:
3610:
3607:
3606:
3583:
3579:
3564:
3560:
3558:
3555:
3554:
3532:
3529:
3528:
3506:
3503:
3502:
3478:
3476:
3473:
3472:
3453:
3436:
3433:
3432:
3405:
3401:
3386:
3382:
3374:
3371:
3370:
3327:
3323:
3308:
3304:
3295:
3291:
3274:
3270:
3249:
3245:
3230:
3226:
3225:
3221:
3219:
3216:
3215:
3164:
3161:
3160:
3123:
3120:
3119:
3082:
3079:
3078:
3041:
3038:
3037:
3009:
3006:
3005:
2950:
2947:
2946:
2910:
2897:
2893:
2880:
2878:
2850:
2831:
2827:
2814:
2812:
2790:
2778:
2774:
2772:
2734:
2730:
2715:
2711:
2710:
2706:
2704:
2701:
2700:
2695:
2684:
2662:Similarly, for
2660:
2618:
2614:
2569:
2565:
2525:
2517:
2515:
2513:
2510:
2509:
2465:
2462:
2461:
2424:
2421:
2420:
2392:
2389:
2388:
2356:
2352:
2341:
2338:
2337:
2282:
2278:
2276:
2273:
2272:
2244:
2205:
2201:
2199:
2196:
2195:
2158:
2154:
2130:
2126:
2086:
2078:
2076:
2050:
2046:
2045:
2041:
2039:
2036:
2035:
2009:
2005:
2003:
2000:
1999:
1970:
1966:
1957:
1953:
1938:
1934:
1932:
1929:
1928:
1907:
1903:
1888:
1884:
1882:
1879:
1878:
1858:
1854:
1845:
1841:
1832:
1828:
1826:
1823:
1822:
1805:
1801:
1799:
1796:
1795:
1774:
1770:
1755:
1751:
1742:
1738:
1736:
1733:
1732:
1706:
1701:
1676:
1672:
1657:
1653:
1616:
1612:
1597:
1593:
1551:
1547:
1546:
1542:
1540:
1537:
1536:
1516:
1512:
1497:
1493:
1468:
1464:
1449:
1445:
1403:
1399:
1398:
1394:
1392:
1389:
1388:
1356:
1352:
1337:
1333:
1312:
1308:
1293:
1289:
1271:
1267:
1227:
1219:
1217:
1191:
1187:
1186:
1182:
1180:
1177:
1176:
1147:
1143:
1128:
1124:
1109:
1105:
1090:
1086:
1076:
1063:
1062:
1061:
1055:
1044:
1014:
1010:
1009:
1005:
1003:
1000:
999:
966:
962:
960:
957:
956:
953:
915:
906:
891:
882:
875:
865:
856:
845:
837:
833:
829:
820:
813:
805:
771:
767:
765:
762:
761:
738:
734:
732:
729:
728:
718:
708:
679:
675:
673:
670:
669:
663:
652:
642:
602:
598:
583:
579:
566:
562:
547:
543:
521:
520:
518:
515:
514:
480:
476:
461:
457:
435:
431:
429:
426:
425:
407:
406:
400:
373:
369:
354:
350:
328:
324:
322:
319:
318:
293:
292:
284:
282:
246:
242:
215:
211:
184:
180:
153:
149:
147:
144:
143:
129:
71:rank statistics
59:order statistic
28:
23:
22:
15:
12:
11:
5:
12732:
12722:
12721:
12716:
12711:
12694:
12693:
12691:
12690:
12678:
12666:
12652:
12639:
12636:
12635:
12632:
12631:
12628:
12627:
12625:
12624:
12619:
12614:
12609:
12604:
12598:
12596:
12590:
12589:
12587:
12586:
12581:
12576:
12571:
12566:
12561:
12556:
12551:
12546:
12541:
12535:
12533:
12527:
12526:
12524:
12523:
12518:
12513:
12504:
12499:
12494:
12488:
12486:
12480:
12479:
12477:
12476:
12471:
12466:
12457:
12455:Bioinformatics
12451:
12449:
12439:
12438:
12426:
12425:
12422:
12421:
12418:
12417:
12414:
12413:
12411:
12410:
12404:
12402:
12398:
12397:
12395:
12394:
12388:
12386:
12380:
12379:
12377:
12376:
12371:
12366:
12361:
12355:
12353:
12344:
12338:
12337:
12334:
12333:
12331:
12330:
12325:
12320:
12315:
12310:
12304:
12302:
12296:
12295:
12293:
12292:
12287:
12282:
12274:
12269:
12264:
12263:
12262:
12260:partial (PACF)
12251:
12249:
12243:
12242:
12240:
12239:
12234:
12229:
12221:
12216:
12210:
12208:
12207:Specific tests
12204:
12203:
12201:
12200:
12195:
12190:
12185:
12180:
12175:
12170:
12165:
12159:
12157:
12150:
12144:
12143:
12141:
12140:
12139:
12138:
12137:
12136:
12121:
12120:
12119:
12109:
12107:Classification
12104:
12099:
12094:
12089:
12084:
12079:
12073:
12071:
12065:
12064:
12062:
12061:
12056:
12054:McNemar's test
12051:
12046:
12041:
12036:
12030:
12028:
12018:
12017:
11993:
11992:
11989:
11988:
11985:
11984:
11982:
11981:
11976:
11971:
11966:
11960:
11958:
11952:
11951:
11949:
11948:
11932:
11926:
11924:
11918:
11917:
11915:
11914:
11909:
11904:
11899:
11894:
11892:Semiparametric
11889:
11884:
11878:
11876:
11872:
11871:
11869:
11868:
11863:
11858:
11853:
11847:
11845:
11839:
11838:
11836:
11835:
11830:
11825:
11820:
11815:
11809:
11807:
11801:
11800:
11798:
11797:
11792:
11787:
11782:
11776:
11774:
11764:
11763:
11760:
11759:
11754:
11748:
11740:
11739:
11736:
11735:
11732:
11731:
11729:
11728:
11727:
11726:
11716:
11711:
11706:
11705:
11704:
11699:
11688:
11686:
11680:
11679:
11676:
11675:
11673:
11672:
11667:
11666:
11665:
11657:
11649:
11633:
11630:(MannâWhitney)
11625:
11624:
11623:
11610:
11609:
11608:
11597:
11595:
11589:
11588:
11586:
11585:
11584:
11583:
11578:
11573:
11563:
11558:
11555:(ShapiroâWilk)
11550:
11545:
11540:
11535:
11530:
11522:
11516:
11514:
11508:
11507:
11505:
11504:
11496:
11487:
11475:
11469:
11467:Specific tests
11463:
11462:
11459:
11458:
11456:
11455:
11450:
11445:
11439:
11437:
11431:
11430:
11428:
11427:
11422:
11421:
11420:
11410:
11409:
11408:
11398:
11392:
11390:
11384:
11383:
11381:
11380:
11379:
11378:
11373:
11363:
11358:
11353:
11348:
11343:
11337:
11335:
11329:
11328:
11326:
11325:
11320:
11319:
11318:
11313:
11312:
11311:
11306:
11291:
11290:
11289:
11284:
11279:
11274:
11263:
11261:
11252:
11246:
11245:
11243:
11242:
11237:
11232:
11231:
11230:
11220:
11215:
11214:
11213:
11203:
11202:
11201:
11196:
11191:
11181:
11176:
11171:
11170:
11169:
11164:
11159:
11143:
11142:
11141:
11136:
11131:
11121:
11120:
11119:
11114:
11104:
11103:
11102:
11092:
11091:
11090:
11080:
11075:
11070:
11064:
11062:
11052:
11051:
11039:
11038:
11035:
11034:
11031:
11030:
11028:
11027:
11022:
11017:
11012:
11006:
11004:
10998:
10997:
10995:
10994:
10989:
10984:
10978:
10976:
10972:
10971:
10969:
10968:
10963:
10958:
10953:
10948:
10943:
10938:
10932:
10930:
10924:
10923:
10921:
10920:
10918:Standard error
10915:
10910:
10905:
10904:
10903:
10898:
10887:
10885:
10879:
10878:
10876:
10875:
10870:
10865:
10860:
10855:
10850:
10848:Optimal design
10845:
10840:
10834:
10832:
10822:
10821:
10809:
10808:
10805:
10804:
10801:
10800:
10798:
10797:
10792:
10787:
10782:
10777:
10772:
10767:
10762:
10757:
10752:
10747:
10742:
10737:
10732:
10727:
10721:
10719:
10713:
10712:
10710:
10709:
10704:
10703:
10702:
10697:
10687:
10682:
10676:
10674:
10668:
10667:
10665:
10664:
10659:
10654:
10648:
10646:
10645:Summary tables
10642:
10641:
10639:
10638:
10632:
10630:
10624:
10623:
10620:
10619:
10617:
10616:
10615:
10614:
10609:
10604:
10594:
10588:
10586:
10580:
10579:
10577:
10576:
10571:
10566:
10561:
10556:
10551:
10546:
10540:
10538:
10532:
10531:
10529:
10528:
10523:
10518:
10517:
10516:
10511:
10506:
10501:
10496:
10491:
10486:
10481:
10479:Contraharmonic
10476:
10471:
10460:
10458:
10449:
10439:
10438:
10426:
10425:
10423:
10422:
10417:
10411:
10408:
10407:
10400:
10399:
10392:
10385:
10377:
10371:
10370:
10364:
10344:
10332:
10331:External links
10329:
10326:
10325:
10319:
10293:
10264:(1): 148â164.
10254:Willcox, Karen
10244:
10235:
10215:(4): 377â408.
10190:
10163:
10150:(3): 191â231.
10125:
10119:
10093:
10055:
10048:
10025:
10018:
9998:
9991:
9964:
9963:
9961:
9958:
9955:
9954:
9909:
9907:
9900:
9895:
9894:
9889:
9884:
9879:
9874:
9869:
9864:
9859:
9852:
9849:
9848:
9847:
9842:
9837:
9831:
9826:
9820:
9815:
9810:
9808:BRS-inequality
9805:
9800:
9793:
9790:
9754:
9751:
9750:
9749:
9734:
9730:
9724:
9721:
9718:
9714:
9710:
9707:
9704:
9701:
9698:
9695:
9692:
9689:
9686:
9683:
9678:
9674:
9670:
9667:
9664:
9661:
9658:
9655:
9652:
9649:
9646:
9643:
9640:
9637:
9634:
9629:
9626:
9623:
9619:
9615:
9612:
9609:
9606:
9603:
9598:
9594:
9590:
9587:
9584:
9581:
9578:
9575:
9572:
9568:
9561:
9556:
9553:
9548:
9540:
9537:
9534:
9529:
9526:
9523:
9519:
9515:
9512:
9510:
9508:
9505:
9501:
9495:
9492:
9489:
9485:
9479:
9475:
9471:
9466:
9462:
9456:
9452:
9448:
9443:
9439:
9435:
9432:
9427:
9424:
9421:
9417:
9411:
9407:
9403:
9398:
9394:
9390:
9385:
9380:
9376:
9371:
9364:
9359:
9356:
9351:
9343:
9340:
9337:
9332:
9329:
9326:
9322:
9318:
9315:
9313:
9311:
9308:
9305:
9302:
9299:
9294:
9291:
9288:
9284:
9280:
9277:
9274:
9271:
9268:
9265:
9260:
9257:
9254:
9250:
9246:
9243:
9240:
9237:
9235:
9233:
9230:
9227:
9222:
9219:
9216:
9212:
9208:
9205:
9202:
9201:
9176:
9173:
9170:
9166:
9154:
9153:
9138:
9133:
9130:
9127:
9123:
9117:
9113:
9109:
9104:
9100:
9094:
9090:
9086:
9081:
9077:
9073:
9067:
9062:
9059:
9054:
9046:
9043:
9040:
9035:
9032:
9029:
9025:
9021:
9018:
9016:
9014:
9011:
9008:
9005:
8997:
8994:
8991:
8983:
8980:
8977:
8974:
8972:
8970:
8967:
8964:
8961:
8953:
8945:
8942:
8939:
8936:
8934:
8932:
8929:
8926:
8921:
8918:
8915:
8911:
8907:
8904:
8901:
8900:
8877:
8874:
8871:
8866:
8863:
8860:
8856:
8852:
8849:
8838:
8837:
8822:
8817:
8814:
8811:
8807:
8801:
8797:
8793:
8788:
8784:
8780:
8775:
8770:
8766:
8759:
8754:
8751:
8746:
8738:
8735:
8732:
8727:
8724:
8721:
8717:
8713:
8710:
8708:
8706:
8703:
8700:
8697:
8689:
8686:
8683:
8675:
8672:
8669:
8666:
8664:
8662:
8659:
8656:
8653:
8645:
8637:
8634:
8631:
8628:
8626:
8624:
8621:
8618:
8613:
8610:
8607:
8603:
8599:
8596:
8593:
8592:
8563:
8551:
8550:
8539:
8536:
8533:
8530:
8527:
8524:
8521:
8518:
8515:
8512:
8509:
8506:
8503:
8500:
8497:
8492:
8488:
8479:
8476:
8473:
8470:
8467:
8464:
8461:
8458:
8455:
8452:
8449:
8446:
8443:
8438:
8434:
8427:
8424:
8421:
8418:
8415:
8412:
8409:
8406:
8403:
8400:
8397:
8394:
8391:
8388:
8385:
8382:
8379:
8376:
8371:
8367:
8337:
8316:
8313:
8310:
8307:
8284:
8281:
8278:
8275:
8253:
8249:
8245:
8242:
8239:
8234:
8230:
8226:
8221:
8217:
8204:
8201:
8170:
8167:
8132:
8128:
8124:
8119:
8115:
8111:
8108:
8105:
8102:
8098:
8093:
8088:
8081:
8078:
8071:
8066:
8062:
8037:
8033:
8027:
8024:
8020:
8010:
8006:
8000:
7997:
7994:
7990:
7986:
7981:
7977:
7973:
7968:
7964:
7939:
7917:
7913:
7890:
7887:
7883:
7857:
7853:
7849:
7846:
7843:
7840:
7814:
7811:
7808:
7805:
7802:
7776:
7773:
7748:
7744:
7721:
7717:
7694:
7691:
7687:
7664:
7660:
7656:
7651:
7647:
7622:
7618:
7614:
7609:
7604:
7600:
7579:
7574:
7571:
7568:
7564:
7560:
7557:
7554:
7551:
7546:
7542:
7531:
7516:
7511:
7508:
7505:
7501:
7495:
7488:
7485:
7478:
7458:
7455:
7452:
7449:
7446:
7443:
7440:
7418:
7413:
7410:
7407:
7403:
7397:
7393:
7389:
7380:observations.
7369:
7359:
7340:
7336:
7332:
7329:
7326:
7323:
7320:
7317:
7314:
7311:
7308:
7305:
7302:
7299:
7296:
7291:
7287:
7264:
7260:
7239:
7228:
7227:
7216:
7213:
7209:
7206:
7203:
7198:
7195:
7192:
7188:
7184:
7181:
7178:
7174:
7171:
7165:
7160:
7156:
7149:
7146:
7143:
7140:
7137:
7134:
7131:
7128:
7125:
7122:
7118:
7113:
7107:
7104:
7101:
7098:
7095:
7092:
7089:
7086:
7083:
7079:
7074:
7071:
7066:
7063:
7060:
7056:
7052:
7049:
7026:
7004:
7001:
6998:
6994:
6968:
6964:
6961:
6958:
6953:
6949:
6942:
6939:
6934:
6930:
6926:
6921:
6917:
6896:
6893:
6890:
6885:
6881:
6877:
6872:
6868:
6864:
6861:
6856:
6852:
6848:
6845:
6842:
6837:
6833:
6829:
6826:
6823:
6820:
6815:
6811:
6789:
6783:
6779:
6775:
6770:
6766:
6761:
6757:
6752:
6748:
6725:
6721:
6698:
6694:
6681:
6678:
6648:
6643:
6642:
6631:
6626:
6622:
6616:
6613:
6610:
6605:
6602:
6599:
6596:
6593:
6589:
6585:
6582:
6578:
6573:
6569:
6563:
6558:
6555:
6552:
6548:
6544:
6541:
6527:
6526:
6515:
6509:
6506:
6503:
6499:
6486:
6480:
6470:
6467:
6464:
6461:
6458:
6455:
6452:
6449:
6446:
6443:
6428:
6425:
6362:
6361:
6349:
6340:
6336:
6332:
6329:
6326:
6323:
6318:
6315:
6311:
6307:
6304:
6301:
6298:
6293:
6290:
6287:
6284:
6281:
6278:
6272:
6269:
6266:
6263:
6258:
6255:
6251:
6246:
6242:
6239:
6236:
6231:
6228:
6225:
6222:
6219:
6216:
6212:
6185:
6184:
6173:
6169:
6163:
6159:
6156:
6153:
6150:
6147:
6144:
6138:
6135:
6131:
6127:
6124:
6121:
6116:
6113:
6110:
6107:
6104:
6101:
6097:
6069:
6066:
6061:
6060:
6049:
6046:
6043:
6040:
6035:
6032:
6027:
6022:
6018:
6014:
6010:
6006:
6003:
5999:
5992:
5987:
5984:
5979:
5973:
5967:
5962:
5959:
5954:
5948:
5942:
5937:
5934:
5929:
5922:
5902:
5901:
5890:
5887:
5884:
5881:
5876:
5873:
5868:
5863:
5859:
5855:
5851:
5847:
5844:
5838:
5833:
5830:
5825:
5803:
5800:
5791:
5788:
5787:
5786:
5775:
5770:
5766:
5762:
5759:
5756:
5751:
5747:
5743:
5738:
5734:
5713:
5708:
5704:
5700:
5695:
5691:
5687:
5684:
5679:
5675:
5671:
5666:
5662:
5658:
5655:
5652:
5649:
5644:
5640:
5636:
5633:
5630:
5625:
5621:
5617:
5610:
5607:
5604:
5600:
5596:
5593:
5590:
5585:
5582:
5579:
5575:
5570:
5558:
5557:
5546:
5543:
5540:
5520:
5517:
5514:
5509:
5505:
5501:
5498:
5495:
5490:
5486:
5480:
5477:
5474:
5470:
5466:
5463:
5460:
5455:
5451:
5447:
5444:
5441:
5436:
5433:
5430:
5427:
5424:
5420:
5416:
5413:
5410:
5405:
5401:
5397:
5394:
5391:
5388:
5383:
5379:
5375:
5370:
5367:
5364:
5360:
5356:
5353:
5350:
5345:
5341:
5337:
5331:
5328:
5325:
5322:
5319:
5316:
5313:
5310:
5307:
5304:
5301:
5298:
5295:
5292:
5289:
5286:
5283:
5280:
5277:
5274:
5269:
5266:
5260:
5257:
5254:
5251:
5248:
5245:
5238:
5235:
5232:
5228:
5224:
5219:
5216:
5213:
5209:
5204:
5192:
5191:
5180:
5177:
5174:
5169:
5165:
5159:
5156:
5153:
5149:
5145:
5142:
5139:
5134:
5130:
5126:
5123:
5120:
5115:
5112:
5109:
5105:
5101:
5098:
5095:
5090:
5086:
5082:
5076:
5073:
5070:
5067:
5064:
5061:
5058:
5055:
5052:
5049:
5046:
5043:
5038:
5035:
5029:
5026:
5023:
5020:
5013:
5010:
5007:
5003:
4998:
4975:
4974:
4963:
4960:
4956:
4953:
4950:
4945:
4941:
4937:
4934:
4931:
4917:
4916:
4905:
4902:
4899:
4894:
4890:
4886:
4883:
4860:
4857:
4853:
4850:
4847:
4842:
4838:
4834:
4831:
4828:
4825:
4820:
4816:
4812:
4794:
4787:
4784:
4771:
4768:
4757:
4751:
4750:
4749:
4748:
4736:
4729:
4726:
4723:
4720:
4717:
4711:
4707:
4699:
4694:
4691:
4688:
4684:
4679:
4673:
4670:
4661:
4656:
4647:
4644:
4641:
4637:
4618:= 1,2,3, ...,
4607:
4578:
4574:
4570:
4567:
4564:
4561:
4556:
4552:
4548:
4543:
4539:
4526:
4523:
4510:
4507:
4504:
4501:
4498:
4495:
4492:
4489:
4486:
4483:
4480:
4477:
4474:
4471:
4468:
4465:
4462:
4459:
4456:
4433:
4430:
4427:
4424:
4421:
4416:
4412:
4408:
4405:
4402:
4399:
4394:
4391:
4388:
4385:
4382:
4379:
4376:
4373:
4370:
4367:
4364:
4361:
4358:
4355:
4352:
4349:
4343:
4340:
4337:
4334:
4331:
4328:
4308:
4303:
4300:
4297:
4293:
4289:
4284:
4281:
4278:
4274:
4270:
4267:
4264:
4261:
4258:
4255:
4249:
4246:
4243:
4240:
4237:
4232:
4228:
4224:
4221:
4218:
4215:
4210:
4207:
4204:
4201:
4198:
4195:
4192:
4189:
4183:
4177:
4174:
4171:
4168:
4165:
4160:
4156:
4152:
4149:
4146:
4143:
4138:
4135:
4132:
4129:
4126:
4123:
4120:
4117:
4111:
4108:
4103:
4100:
4097:
4093:
4089:
4084:
4081:
4078:
4074:
4070:
4067:
4064:
4061:
4058:
4055:
4052:
4047:
4044:
4041:
4037:
4033:
4030:
4027:
4024:
4021:
4016:
4013:
4010:
4006:
4002:
3999:
3996:
3993:
3990:
3985:
3982:
3979:
3975:
3971:
3966:
3963:
3960:
3956:
3952:
3949:
3946:
3923:
3920:
3917:
3914:
3911:
3906:
3902:
3898:
3895:
3892:
3889:
3884:
3881:
3878:
3875:
3872:
3869:
3866:
3863:
3857:
3854:
3849:
3846:
3843:
3839:
3835:
3830:
3827:
3824:
3820:
3816:
3813:
3810:
3790:
3787:
3784:
3781:
3778:
3775:
3772:
3769:
3766:
3763:
3760:
3757:
3754:
3751:
3748:
3745:
3742:
3739:
3734:
3731:
3728:
3724:
3720:
3715:
3712:
3709:
3705:
3682:
3679:
3676:
3672:
3668:
3663:
3660:
3657:
3653:
3632:
3629:
3626:
3623:
3620:
3617:
3614:
3592:
3589:
3586:
3582:
3578:
3573:
3570:
3567:
3563:
3539:
3536:
3516:
3513:
3510:
3488:
3485:
3482:
3460:
3456:
3452:
3449:
3446:
3443:
3440:
3429:BRS-inequality
3416:
3413:
3408:
3404:
3400:
3397:
3394:
3389:
3385:
3381:
3378:
3359:
3358:
3347:
3344:
3341:
3338:
3335:
3330:
3326:
3322:
3319:
3316:
3311:
3307:
3303:
3298:
3294:
3290:
3283:
3280:
3277:
3273:
3269:
3266:
3263:
3258:
3255:
3252:
3248:
3244:
3239:
3236:
3233:
3229:
3224:
3200:respectively.
3189:
3186:
3183:
3180:
3177:
3174:
3171:
3168:
3148:
3145:
3142:
3139:
3136:
3133:
3130:
3127:
3107:
3104:
3101:
3098:
3095:
3092:
3089:
3086:
3066:
3063:
3060:
3057:
3054:
3051:
3048:
3045:
3025:
3022:
3019:
3016:
3013:
2973:
2970:
2967:
2963:
2960:
2957:
2954:
2943:
2942:
2928:
2925:
2922:
2919:
2916:
2913:
2906:
2903:
2900:
2896:
2892:
2889:
2886:
2883:
2874:
2871:
2868:
2865:
2862:
2859:
2856:
2853:
2846:
2843:
2840:
2837:
2834:
2830:
2826:
2823:
2820:
2817:
2808:
2805:
2802:
2799:
2796:
2793:
2787:
2784:
2781:
2777:
2771:
2768:
2765:
2762:
2759:
2756:
2753:
2750:
2743:
2740:
2737:
2733:
2729:
2724:
2721:
2718:
2714:
2709:
2689:
2678:
2659:
2656:
2641:
2640:
2627:
2624:
2621:
2617:
2613:
2610:
2607:
2604:
2601:
2598:
2595:
2592:
2589:
2586:
2583:
2578:
2575:
2572:
2568:
2561:
2558:
2555:
2552:
2549:
2546:
2543:
2540:
2537:
2534:
2531:
2528:
2523:
2520:
2490:
2487:
2484:
2481:
2478:
2475:
2472:
2469:
2449:
2446:
2443:
2440:
2437:
2434:
2431:
2428:
2408:
2405:
2402:
2399:
2396:
2364:
2359:
2355:
2351:
2348:
2345:
2332: + d
2304:to be between
2291:
2288:
2285:
2281:
2269:
2268:
2257:
2254:
2251:
2247:
2243:
2240:
2237:
2234:
2231:
2228:
2225:
2222:
2219:
2214:
2211:
2208:
2204:
2181:
2180:
2167:
2164:
2161:
2157:
2153:
2150:
2147:
2144:
2139:
2136:
2133:
2129:
2122:
2119:
2116:
2113:
2110:
2107:
2104:
2101:
2098:
2095:
2092:
2089:
2084:
2081:
2075:
2072:
2069:
2066:
2059:
2056:
2053:
2049:
2044:
2018:
2015:
2012:
2008:
1984:
1979:
1976:
1973:
1969:
1965:
1960:
1956:
1952:
1947:
1944:
1941:
1937:
1910:
1906:
1902:
1899:
1896:
1891:
1887:
1866:
1861:
1857:
1853:
1848:
1844:
1840:
1835:
1831:
1808:
1804:
1777:
1773:
1769:
1766:
1763:
1758:
1754:
1750:
1745:
1741:
1705:
1702:
1700:
1697:
1693:
1692:
1679:
1675:
1671:
1668:
1665:
1660:
1656:
1652:
1649:
1646:
1643:
1640:
1637:
1634:
1631:
1628:
1625:
1619:
1615:
1611:
1608:
1605:
1600:
1596:
1591:
1588:
1585:
1582:
1579:
1576:
1573:
1570:
1567:
1560:
1557:
1554:
1550:
1545:
1533:
1532:
1519:
1515:
1511:
1508:
1505:
1500:
1496:
1492:
1489:
1486:
1483:
1480:
1477:
1471:
1467:
1463:
1460:
1457:
1452:
1448:
1443:
1440:
1437:
1434:
1431:
1428:
1425:
1422:
1419:
1412:
1409:
1406:
1402:
1397:
1382:
1381:
1370:
1365:
1362:
1359:
1355:
1351:
1348:
1345:
1340:
1336:
1332:
1329:
1326:
1321:
1318:
1315:
1311:
1307:
1304:
1301:
1296:
1292:
1288:
1285:
1282:
1279:
1274:
1270:
1263:
1260:
1257:
1254:
1251:
1248:
1245:
1242:
1239:
1236:
1233:
1230:
1225:
1222:
1216:
1213:
1210:
1207:
1200:
1197:
1194:
1190:
1185:
1170:
1169:
1156:
1153:
1150:
1146:
1142:
1139:
1136:
1131:
1127:
1123:
1120:
1117:
1112:
1108:
1104:
1101:
1098:
1093:
1089:
1085:
1079:
1074:
1071:
1066:
1058:
1053:
1050:
1047:
1043:
1039:
1036:
1033:
1030:
1023:
1020:
1017:
1013:
1008:
980:
977:
974:
969:
965:
952:
949:
911:
904:
887:
880:
873:
861:
854:
839:
835:
831:
825:
818:
811:
804:
801:
786:
783:
780:
777:
774:
770:
747:
744:
741:
737:
694:
691:
688:
685:
682:
678:
628:
627:
616:
611:
608:
605:
601:
597:
592:
589:
586:
582:
578:
575:
569:
565:
561:
558:
555:
550:
546:
541:
536:
533:
530:
527:
524:
504:
503:
492:
489:
483:
479:
475:
472:
469:
464:
460:
455:
452:
449:
444:
441:
438:
434:
394:
393:
382:
376:
372:
368:
365:
362:
357:
353:
348:
345:
342:
337:
334:
331:
327:
279:
278:
266:
263:
260:
255:
252:
249:
245:
235:
232:
229:
224:
221:
218:
214:
204:
201:
198:
193:
190:
187:
183:
173:
170:
167:
162:
159:
156:
152:
137:
136:
128:
125:
109:random samples
26:
9:
6:
4:
3:
2:
12731:
12720:
12717:
12715:
12712:
12710:
12707:
12706:
12704:
12689:
12688:
12679:
12677:
12676:
12667:
12665:
12664:
12659:
12653:
12651:
12650:
12641:
12640:
12637:
12623:
12620:
12618:
12617:Geostatistics
12615:
12613:
12610:
12608:
12605:
12603:
12600:
12599:
12597:
12595:
12591:
12585:
12584:Psychometrics
12582:
12580:
12577:
12575:
12572:
12570:
12567:
12565:
12562:
12560:
12557:
12555:
12552:
12550:
12547:
12545:
12542:
12540:
12537:
12536:
12534:
12532:
12528:
12522:
12519:
12517:
12514:
12512:
12508:
12505:
12503:
12500:
12498:
12495:
12493:
12490:
12489:
12487:
12485:
12481:
12475:
12472:
12470:
12467:
12465:
12461:
12458:
12456:
12453:
12452:
12450:
12448:
12447:Biostatistics
12444:
12440:
12436:
12431:
12427:
12409:
12408:Log-rank test
12406:
12405:
12403:
12399:
12393:
12390:
12389:
12387:
12385:
12381:
12375:
12372:
12370:
12367:
12365:
12362:
12360:
12357:
12356:
12354:
12352:
12348:
12345:
12343:
12339:
12329:
12326:
12324:
12321:
12319:
12316:
12314:
12311:
12309:
12306:
12305:
12303:
12301:
12297:
12291:
12288:
12286:
12283:
12281:
12279:(BoxâJenkins)
12275:
12273:
12270:
12268:
12265:
12261:
12258:
12257:
12256:
12253:
12252:
12250:
12248:
12244:
12238:
12235:
12233:
12232:DurbinâWatson
12230:
12228:
12222:
12220:
12217:
12215:
12214:DickeyâFuller
12212:
12211:
12209:
12205:
12199:
12196:
12194:
12191:
12189:
12188:Cointegration
12186:
12184:
12181:
12179:
12176:
12174:
12171:
12169:
12166:
12164:
12163:Decomposition
12161:
12160:
12158:
12154:
12151:
12149:
12145:
12135:
12132:
12131:
12130:
12127:
12126:
12125:
12122:
12118:
12115:
12114:
12113:
12110:
12108:
12105:
12103:
12100:
12098:
12095:
12093:
12090:
12088:
12085:
12083:
12080:
12078:
12075:
12074:
12072:
12070:
12066:
12060:
12057:
12055:
12052:
12050:
12047:
12045:
12042:
12040:
12037:
12035:
12034:Cohen's kappa
12032:
12031:
12029:
12027:
12023:
12019:
12015:
12011:
12007:
12003:
11998:
11994:
11980:
11977:
11975:
11972:
11970:
11967:
11965:
11962:
11961:
11959:
11957:
11953:
11947:
11943:
11939:
11933:
11931:
11928:
11927:
11925:
11923:
11919:
11913:
11910:
11908:
11905:
11903:
11900:
11898:
11895:
11893:
11890:
11888:
11887:Nonparametric
11885:
11883:
11880:
11879:
11877:
11873:
11867:
11864:
11862:
11859:
11857:
11854:
11852:
11849:
11848:
11846:
11844:
11840:
11834:
11831:
11829:
11826:
11824:
11821:
11819:
11816:
11814:
11811:
11810:
11808:
11806:
11802:
11796:
11793:
11791:
11788:
11786:
11783:
11781:
11778:
11777:
11775:
11773:
11769:
11765:
11758:
11755:
11753:
11750:
11749:
11745:
11741:
11725:
11722:
11721:
11720:
11717:
11715:
11712:
11710:
11707:
11703:
11700:
11698:
11695:
11694:
11693:
11690:
11689:
11687:
11685:
11681:
11671:
11668:
11664:
11658:
11656:
11650:
11648:
11642:
11641:
11640:
11637:
11636:Nonparametric
11634:
11632:
11626:
11622:
11619:
11618:
11617:
11611:
11607:
11606:Sample median
11604:
11603:
11602:
11599:
11598:
11596:
11594:
11590:
11582:
11579:
11577:
11574:
11572:
11569:
11568:
11567:
11564:
11562:
11559:
11557:
11551:
11549:
11546:
11544:
11541:
11539:
11536:
11534:
11531:
11529:
11527:
11523:
11521:
11518:
11517:
11515:
11513:
11509:
11503:
11501:
11497:
11495:
11493:
11488:
11486:
11481:
11477:
11476:
11473:
11470:
11468:
11464:
11454:
11451:
11449:
11446:
11444:
11441:
11440:
11438:
11436:
11432:
11426:
11423:
11419:
11416:
11415:
11414:
11411:
11407:
11404:
11403:
11402:
11399:
11397:
11394:
11393:
11391:
11389:
11385:
11377:
11374:
11372:
11369:
11368:
11367:
11364:
11362:
11359:
11357:
11354:
11352:
11349:
11347:
11344:
11342:
11339:
11338:
11336:
11334:
11330:
11324:
11321:
11317:
11314:
11310:
11307:
11305:
11302:
11301:
11300:
11297:
11296:
11295:
11292:
11288:
11285:
11283:
11280:
11278:
11275:
11273:
11270:
11269:
11268:
11265:
11264:
11262:
11260:
11256:
11253:
11251:
11247:
11241:
11238:
11236:
11233:
11229:
11226:
11225:
11224:
11221:
11219:
11216:
11212:
11211:loss function
11209:
11208:
11207:
11204:
11200:
11197:
11195:
11192:
11190:
11187:
11186:
11185:
11182:
11180:
11177:
11175:
11172:
11168:
11165:
11163:
11160:
11158:
11152:
11149:
11148:
11147:
11144:
11140:
11137:
11135:
11132:
11130:
11127:
11126:
11125:
11122:
11118:
11115:
11113:
11110:
11109:
11108:
11105:
11101:
11098:
11097:
11096:
11093:
11089:
11086:
11085:
11084:
11081:
11079:
11076:
11074:
11071:
11069:
11066:
11065:
11063:
11061:
11057:
11053:
11049:
11044:
11040:
11026:
11023:
11021:
11018:
11016:
11013:
11011:
11008:
11007:
11005:
11003:
10999:
10993:
10990:
10988:
10985:
10983:
10980:
10979:
10977:
10973:
10967:
10964:
10962:
10959:
10957:
10954:
10952:
10949:
10947:
10944:
10942:
10939:
10937:
10934:
10933:
10931:
10929:
10925:
10919:
10916:
10914:
10913:Questionnaire
10911:
10909:
10906:
10902:
10899:
10897:
10894:
10893:
10892:
10889:
10888:
10886:
10884:
10880:
10874:
10871:
10869:
10866:
10864:
10861:
10859:
10856:
10854:
10851:
10849:
10846:
10844:
10841:
10839:
10836:
10835:
10833:
10831:
10827:
10823:
10819:
10814:
10810:
10796:
10793:
10791:
10788:
10786:
10783:
10781:
10778:
10776:
10773:
10771:
10768:
10766:
10763:
10761:
10758:
10756:
10753:
10751:
10748:
10746:
10743:
10741:
10740:Control chart
10738:
10736:
10733:
10731:
10728:
10726:
10723:
10722:
10720:
10718:
10714:
10708:
10705:
10701:
10698:
10696:
10693:
10692:
10691:
10688:
10686:
10683:
10681:
10678:
10677:
10675:
10673:
10669:
10663:
10660:
10658:
10655:
10653:
10650:
10649:
10647:
10643:
10637:
10634:
10633:
10631:
10629:
10625:
10613:
10610:
10608:
10605:
10603:
10600:
10599:
10598:
10595:
10593:
10590:
10589:
10587:
10585:
10581:
10575:
10572:
10570:
10567:
10565:
10562:
10560:
10557:
10555:
10552:
10550:
10547:
10545:
10542:
10541:
10539:
10537:
10533:
10527:
10524:
10522:
10519:
10515:
10512:
10510:
10507:
10505:
10502:
10500:
10497:
10495:
10492:
10490:
10487:
10485:
10482:
10480:
10477:
10475:
10472:
10470:
10467:
10466:
10465:
10462:
10461:
10459:
10457:
10453:
10450:
10448:
10444:
10440:
10436:
10431:
10427:
10421:
10418:
10416:
10413:
10412:
10409:
10405:
10398:
10393:
10391:
10386:
10384:
10379:
10378:
10375:
10369:
10365:
10359:
10358:
10353:
10350:
10345:
10342:
10338:
10335:
10334:
10322:
10320:9780471722168
10316:
10312:
10308:
10304:
10297:
10289:
10285:
10281:
10277:
10272:
10267:
10263:
10259:
10255:
10248:
10239:
10223:
10218:
10214:
10210:
10209:
10204:
10200:
10194:
10186:
10182:
10178:
10174:
10167:
10158:
10153:
10149:
10145:
10144:
10139:
10135:
10134:Rényi, Alfréd
10129:
10122:
10120:9780471722168
10116:
10112:
10108:
10104:
10097:
10090:
10088:
10084:
10078:
10074:
10070:
10066:
10059:
10051:
10049:9780387981444
10045:
10041:
10040:
10032:
10030:
10021:
10019:9788131503942
10015:
10011:
10010:
10002:
9994:
9992:9780471722168
9988:
9984:
9980:
9976:
9969:
9965:
9951:
9948:
9940:
9937:December 2010
9930:
9926:
9920:
9919:
9913:
9908:
9899:
9898:
9893:
9890:
9888:
9885:
9883:
9880:
9878:
9875:
9873:
9870:
9868:
9865:
9863:
9860:
9858:
9855:
9854:
9846:
9843:
9841:
9838:
9835:
9832:
9830:
9827:
9824:
9821:
9819:
9816:
9814:
9811:
9809:
9806:
9804:
9801:
9799:
9796:
9795:
9789:
9787:
9783:
9779:
9775:
9770:
9764:
9760:
9732:
9728:
9722:
9719:
9716:
9705:
9699:
9696:
9690:
9684:
9676:
9665:
9659:
9656:
9650:
9644:
9641:
9638:
9632:
9627:
9624:
9621:
9610:
9604:
9596:
9585:
9579:
9576:
9573:
9566:
9554:
9551:
9538:
9535:
9532:
9527:
9524:
9521:
9517:
9513:
9511:
9503:
9499:
9493:
9490:
9487:
9477:
9473:
9464:
9454:
9450:
9446:
9441:
9437:
9430:
9425:
9422:
9419:
9409:
9405:
9401:
9396:
9392:
9383:
9378:
9374:
9369:
9357:
9354:
9341:
9338:
9335:
9330:
9327:
9324:
9320:
9316:
9314:
9306:
9300:
9297:
9289:
9282:
9275:
9272:
9266:
9263:
9255:
9248:
9241:
9238:
9236:
9228:
9225:
9217:
9210:
9203:
9192:
9191:
9190:
9171:
9164:
9136:
9131:
9128:
9125:
9115:
9111:
9102:
9092:
9088:
9084:
9079:
9075:
9060:
9057:
9044:
9041:
9038:
9033:
9030:
9027:
9023:
9019:
9017:
9009:
9003:
8995:
8992:
8989:
8978:
8975:
8973:
8965:
8959:
8951:
8940:
8937:
8935:
8927:
8924:
8916:
8909:
8902:
8891:
8890:
8889:
8872:
8869:
8861:
8854:
8847:
8820:
8815:
8812:
8809:
8799:
8795:
8791:
8786:
8782:
8773:
8768:
8764:
8752:
8749:
8736:
8733:
8730:
8725:
8722:
8719:
8715:
8711:
8709:
8701:
8695:
8687:
8684:
8681:
8670:
8667:
8665:
8657:
8651:
8643:
8632:
8629:
8627:
8619:
8616:
8608:
8601:
8594:
8583:
8582:
8581:
8561:
8537:
8531:
8525:
8522:
8519:
8516:
8510:
8507:
8504:
8498:
8495:
8490:
8486:
8477:
8471:
8465:
8462:
8456:
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8450:
8444:
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8436:
8432:
8425:
8419:
8413:
8410:
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8357:
8356:
8355:
8335:
8311:
8305:
8298:
8279:
8273:
8251:
8247:
8243:
8240:
8237:
8232:
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8224:
8219:
8215:
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8198:
8193:
8189:
8165:
8155:
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8130:
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8100:
8096:
8091:
8086:
8076:
8069:
8064:
8060:
8035:
8031:
8025:
8022:
8018:
8008:
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7995:
7992:
7988:
7984:
7979:
7975:
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7966:
7962:
7953:
7937:
7915:
7911:
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7885:
7881:
7872:
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7844:
7841:
7838:
7831:
7827:
7812:
7806:
7803:
7800:
7793:
7771:
7746:
7742:
7734:subsets with
7719:
7715:
7692:
7689:
7685:
7662:
7658:
7654:
7649:
7645:
7637:3: Create an
7620:
7616:
7612:
7607:
7602:
7598:
7572:
7569:
7566:
7562:
7555:
7552:
7549:
7544:
7540:
7514:
7509:
7506:
7503:
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7483:
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7450:
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7438:
7416:
7411:
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7391:
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7330:
7327:
7324:
7315:
7312:
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7214:
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7102:
7096:
7090:
7087:
7084:
7077:
7072:
7061:
7054:
7047:
7040:
7039:
7038:
7024:
6999:
6992:
6982:
6966:
6959:
6951:
6947:
6940:
6932:
6928:
6919:
6915:
6891:
6888:
6883:
6879:
6870:
6866:
6862:
6854:
6850:
6846:
6843:
6835:
6831:
6827:
6821:
6813:
6809:
6781:
6777:
6773:
6768:
6764:
6755:
6750:
6746:
6723:
6719:
6711:at the point
6696:
6692:
6677:
6675:
6671:
6667:
6663:
6659:
6655:
6651:
6629:
6624:
6620:
6614:
6611:
6608:
6603:
6600:
6597:
6594:
6591:
6587:
6583:
6580:
6576:
6571:
6567:
6561:
6556:
6553:
6550:
6546:
6542:
6539:
6532:
6531:
6530:
6513:
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6501:
6497:
6478:
6465:
6462:
6459:
6456:
6453:
6450:
6447:
6441:
6434:
6433:
6432:
6424:
6422:
6418:
6414:
6410:
6406:
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6375:
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6316:
6313:
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6296:
6288:
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6282:
6276:
6270:
6264:
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6253:
6249:
6244:
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6234:
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6220:
6210:
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6167:
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6119:
6108:
6105:
6095:
6087:
6086:
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6083:
6079:
6075:
6065:
6047:
6041:
6038:
6033:
6030:
6025:
6020:
6012:
6008:
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5985:
5982:
5971:
5960:
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5946:
5935:
5932:
5920:
5912:
5911:
5910:
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5882:
5879:
5874:
5871:
5866:
5861:
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5849:
5845:
5831:
5828:
5813:
5812:
5811:
5807:
5799:
5797:
5773:
5768:
5764:
5760:
5757:
5754:
5749:
5745:
5741:
5736:
5732:
5706:
5702:
5693:
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5685:
5677:
5673:
5664:
5660:
5656:
5653:
5650:
5642:
5638:
5634:
5631:
5628:
5623:
5619:
5605:
5598:
5594:
5591:
5588:
5580:
5573:
5568:
5560:
5559:
5544:
5541:
5538:
5515:
5507:
5503:
5496:
5488:
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5478:
5475:
5472:
5461:
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5449:
5445:
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5434:
5431:
5428:
5425:
5422:
5411:
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5399:
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5381:
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5368:
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5351:
5343:
5339:
5329:
5323:
5320:
5317:
5311:
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5299:
5296:
5293:
5287:
5281:
5278:
5275:
5267:
5264:
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5252:
5249:
5246:
5233:
5226:
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5214:
5207:
5202:
5194:
5193:
5175:
5167:
5163:
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5154:
5151:
5140:
5132:
5128:
5124:
5121:
5113:
5110:
5107:
5096:
5088:
5084:
5074:
5068:
5065:
5062:
5056:
5050:
5047:
5044:
5036:
5033:
5027:
5021:
5008:
5001:
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4988:
4987:
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4961:
4958:
4951:
4943:
4939:
4935:
4932:
4929:
4922:
4921:
4920:
4900:
4892:
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4884:
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4874:
4873:
4872:
4858:
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4848:
4840:
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4832:
4826:
4818:
4814:
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4802:
4797:
4793:
4783:
4781:
4777:
4767:
4765:
4760:
4756:
4734:
4727:
4724:
4721:
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4705:
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4682:
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4627:
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4624:
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4617:
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4598:
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4576:
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4562:
4559:
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4502:
4496:
4493:
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4484:
4481:
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4472:
4469:
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4326:
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4291:
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4272:
4265:
4262:
4259:
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4238:
4230:
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4219:
4216:
4205:
4202:
4199:
4196:
4193:
4187:
4181:
4172:
4169:
4166:
4158:
4150:
4147:
4144:
4133:
4130:
4127:
4124:
4121:
4115:
4109:
4098:
4091:
4087:
4079:
4072:
4065:
4062:
4059:
4056:
4053:
4042:
4035:
4028:
4025:
4022:
4011:
4004:
3997:
3994:
3991:
3980:
3973:
3969:
3961:
3954:
3947:
3944:
3918:
3915:
3912:
3904:
3896:
3893:
3890:
3879:
3876:
3873:
3870:
3867:
3861:
3855:
3844:
3837:
3833:
3825:
3818:
3811:
3808:
3785:
3782:
3776:
3773:
3770:
3764:
3761:
3758:
3755:
3752:
3749:
3743:
3740:
3737:
3729:
3722:
3718:
3710:
3703:
3677:
3670:
3666:
3658:
3651:
3630:
3627:
3624:
3621:
3618:
3615:
3612:
3587:
3580:
3576:
3568:
3561:
3551:
3537:
3534:
3514:
3511:
3508:
3486:
3483:
3480:
3458:
3454:
3450:
3447:
3444:
3441:
3438:
3430:
3414:
3411:
3406:
3402:
3398:
3395:
3392:
3387:
3383:
3379:
3376:
3368:
3364:
3345:
3342:
3339:
3336:
3328:
3324:
3320:
3317:
3314:
3309:
3305:
3301:
3296:
3292:
3278:
3271:
3267:
3264:
3261:
3253:
3246:
3242:
3234:
3227:
3222:
3214:
3213:
3212:
3210:
3206:
3201:
3184:
3181:
3178:
3175:
3172:
3169:
3143:
3140:
3137:
3134:
3131:
3128:
3102:
3099:
3096:
3093:
3090:
3087:
3061:
3058:
3055:
3052:
3049:
3046:
3020:
3017:
3014:
3003:
3000: â
2999:
2995:
2991:
2987:
2968:
2965:
2961:
2958:
2952:
2926:
2920:
2917:
2914:
2904:
2901:
2898:
2890:
2887:
2884:
2872:
2866:
2863:
2860:
2857:
2854:
2844:
2841:
2838:
2835:
2832:
2824:
2821:
2818:
2806:
2800:
2797:
2794:
2785:
2782:
2779:
2775:
2769:
2766:
2763:
2757:
2754:
2751:
2738:
2731:
2727:
2719:
2712:
2707:
2699:
2698:
2697:
2693:
2688:
2682:
2677:
2673:
2669:
2665:
2655:
2653:
2649:
2644:
2625:
2622:
2619:
2611:
2608:
2605:
2602:
2599:
2596:
2590:
2587:
2584:
2581:
2576:
2573:
2570:
2566:
2559:
2553:
2550:
2547:
2541:
2535:
2532:
2529:
2521:
2518:
2508:
2507:
2506:
2505:for details)
2504:
2485:
2482:
2479:
2476:
2473:
2470:
2444:
2441:
2438:
2435:
2432:
2429:
2403:
2400:
2397:
2386:
2383: â
2382:
2378:
2357:
2353:
2349:
2343:
2335:
2331:
2327:
2323:
2319:
2315:
2312: +
2311:
2307:
2286:
2279:
2255:
2249:
2241:
2238:
2235:
2232:
2229:
2223:
2220:
2217:
2209:
2202:
2194:
2193:
2192:
2190:
2186:
2183:that is, the
2165:
2162:
2159:
2151:
2148:
2145:
2137:
2134:
2131:
2127:
2120:
2114:
2111:
2108:
2102:
2096:
2093:
2090:
2082:
2079:
2073:
2067:
2054:
2047:
2042:
2034:
2033:
2032:
2013:
2006:
1996:
1974:
1967:
1958:
1954:
1950:
1942:
1935:
1926:
1908:
1904:
1900:
1897:
1894:
1889:
1885:
1859:
1855:
1846:
1842:
1838:
1833:
1829:
1806:
1802:
1793:
1792:random sample
1775:
1771:
1767:
1764:
1761:
1756:
1752:
1748:
1743:
1739:
1729:
1727:
1723:
1719:
1715:
1714:unit interval
1711:
1696:
1677:
1666:
1658:
1654:
1650:
1647:
1641:
1638:
1635:
1629:
1626:
1617:
1613:
1609:
1606:
1603:
1598:
1594:
1580:
1577:
1574:
1568:
1555:
1548:
1543:
1535:
1534:
1517:
1506:
1498:
1494:
1487:
1481:
1478:
1469:
1465:
1461:
1458:
1455:
1450:
1446:
1432:
1429:
1426:
1420:
1407:
1400:
1395:
1387:
1386:
1385:
1368:
1363:
1360:
1357:
1346:
1338:
1334:
1330:
1327:
1319:
1316:
1313:
1302:
1294:
1290:
1280:
1272:
1268:
1261:
1255:
1252:
1249:
1243:
1237:
1234:
1231:
1223:
1220:
1214:
1208:
1195:
1188:
1183:
1175:
1174:
1173:
1154:
1151:
1148:
1137:
1129:
1125:
1121:
1118:
1110:
1099:
1091:
1087:
1072:
1069:
1056:
1051:
1048:
1045:
1041:
1037:
1031:
1018:
1011:
1006:
998:
997:
996:
994:
975:
967:
963:
948:
946:
942:
938:
934:
929:
927:
923:
919:
914:
910:
903:
899:
895:
890:
886:
879:
872:
867:
864:
860:
853:
849:
843:
828:
824:
817:
810:
800:
781:
778:
775:
768:
742:
735:
725:
721:
716:
711:
689:
686:
683:
676:
666:
659:
655:
650:
645:
639:
637:
633:
614:
606:
599:
595:
587:
580:
576:
567:
563:
559:
556:
553:
548:
544:
513:
512:
511:
509:
490:
481:
477:
473:
470:
467:
462:
458:
447:
439:
432:
424:
423:
422:
420:
416:
410:
403:
397:
374:
370:
366:
363:
360:
355:
351:
340:
332:
325:
317:
316:
315:
313:
309:
305:
300:
296:
287:
264:
261:
258:
250:
243:
233:
230:
227:
219:
212:
202:
199:
196:
188:
181:
171:
168:
165:
157:
150:
142:
141:
140:
134:
133:
132:
124:
122:
118:
114:
110:
106:
101:
99:
95:
94:sample median
91:
87:
82:
80:
76:
72:
68:
64:
60:
56:
52:
44:
40:
36:
32:
19:
12719:Permutations
12685:
12673:
12654:
12647:
12559:Econometrics
12509: /
12492:Chemometrics
12469:Epidemiology
12462: /
12435:Applications
12277:ARIMA model
12224:Q-statistic
12173:Stationarity
12069:Multivariate
12012: /
12008: /
12006:Multivariate
12004: /
11944: /
11940: /
11714:Bayes factor
11613:Signed rank
11525:
11499:
11491:
11479:
11174:Completeness
11087:
11010:Cohort study
10908:Opinion poll
10843:Missing data
10830:Study design
10785:Scatter plot
10707:Scatter plot
10700:Spearman's Ï
10662:Grouped data
10355:
10302:
10296:
10261:
10257:
10247:
10238:
10228:February 26,
10226:. Retrieved
10212:
10206:
10193:
10176:
10172:
10166:
10147:
10141:
10128:
10102:
10096:
10086:
10082:
10080:
10071:(1): 70â81,
10068:
10064:
10058:
10038:
10008:
10001:
9974:
9968:
9943:
9934:
9915:
9785:
9781:
9773:
9768:
9766:
9155:
8888:is given by
8839:
8552:
8206:
8185:
8153:
8149:
7951:
7870:
7829:
7825:
7791:
7707:which holds
7229:
6983:
6683:
6674:delta method
6669:
6665:
6661:
6657:
6646:
6644:
6528:
6430:
6420:
6408:
6398:
6381:
6373:
6365:
6363:
6196:
6192:
6188:
6186:
6077:
6073:
6071:
6062:
5903:
5808:
5805:
5793:
4982:
4978:
4976:
4918:
4795:
4791:
4789:
4773:
4764:Alfréd Rényi
4758:
4754:
4752:
4619:
4615:
4609:
4604:
4600:
4592:
4528:
3552:
3366:
3362:
3360:
3208:
3204:
3202:
3001:
2997:
2993:
2989:
2985:
2944:
2691:
2686:
2680:
2675:
2667:
2663:
2661:
2651:
2647:
2645:
2642:
2384:
2380:
2376:
2333:
2329:
2325:
2321:
2317:
2313:
2309:
2305:
2270:
2184:
2182:
2031:is equal to
1997:
1730:
1707:
1694:
1383:
1171:
992:
954:
930:
912:
908:
901:
888:
884:
877:
870:
868:
862:
858:
851:
848:realizations
841:
826:
822:
815:
808:
806:
723:
719:
709:
664:
657:
653:
643:
640:
629:
508:sample range
505:
414:
408:
401:
398:
395:
307:
303:
301:
294:
285:
280:
138:
130:
102:
83:
66:
58:
54:
48:
38:
12687:WikiProject
12602:Cartography
12564:Jurimetrics
12516:Reliability
12247:Time domain
12226:(LjungâBox)
12148:Time-series
12026:Categorical
12010:Time-series
12002:Categorical
11937:(Bernoulli)
11772:Correlation
11752:Correlation
11548:JarqueâBera
11520:Chi-squared
11282:M-estimator
11235:Asymptotics
11179:Sufficiency
10946:Interaction
10858:Replication
10838:Effect size
10795:Violin plot
10775:Radar chart
10755:Forest plot
10745:Correlogram
10695:Kendall's Ï
10366:C++ source
9929:introducing
9834:L-estimator
8840:Similarly,
7930:within the
7355:jackknifing
6654:exponential
6401:sample mean
5810:median is
1821:. Denoting
918:independent
421:, that is,
135:6, 9, 3, 7,
103:When using
12703:Categories
12554:Demography
12272:ARMA model
12077:Regression
11654:(Friedman)
11615:(Wilcoxon)
11553:Normality
11543:Lilliefors
11490:Student's
11366:Resampling
11240:Robustness
11228:divergence
11218:Efficiency
11156:(monotone)
11151:Likelihood
11068:Population
10901:Stratified
10853:Population
10672:Dependence
10628:Count data
10559:Percentile
10536:Dispersion
10469:Arithmetic
10404:Statistics
10341:PlanetMath
9960:References
9912:references
9867:Percentile
4753:where the
933:continuous
96:and other
51:statistics
11935:Logistic
11702:posterior
11628:Rank sum
11376:Jackknife
11371:Bootstrap
11189:Bootstrap
11124:Parameter
11073:Statistic
10868:Statistic
10780:Run chart
10765:Pie chart
10760:Histogram
10750:Fan chart
10725:Bar chart
10607:L-moments
10494:Geometric
10357:MathWorld
10271:1412.2851
9720:−
9697:−
9642:−
9633:−
9625:−
9577:−
9536:−
9518:∑
9491:−
9431:−
9423:−
9339:−
9321:∑
9273:−
9264:≤
9129:−
9042:−
9024:∑
8993:−
8813:−
8734:−
8716:∑
8685:−
8617:≤
8523:−
8411:−
8241:…
8188:histogram
8169:^
8131:ℓ
8087:ℓ
8080:^
8065:ℓ
8023:ℓ
7989:∑
7980:ℓ
7967:ℓ
7916:ℓ
7886:ℓ
7848:→
7810:→
7801:ℓ
7775:^
7655:×
7570:−
7556:
7504:ℓ
7494:ℓ
7487:^
7442:∈
7406:ℓ
7396:ℓ
7328:−
7286:δ
7187:δ
7155:∫
6933:∗
6889:−
6884:∗
6855:∗
6782:∗
6774:−
6724:∗
6588:∑
6547:∑
6463:−
6403:, by the
6314:−
6286:−
6254:−
6235:∼
6227:⌉
6218:⌈
6152:−
6120:∼
6112:⌉
6103:⌈
6045:%
6039:≈
5886:%
5880:≈
5796:quantiles
5761:≤
5758:⋯
5755:≤
5742:≤
5686:⋯
5632:…
5592:…
5542:≤
5476:−
5446:−
5432:−
5426:−
5396:−
5366:−
5321:−
5303:−
5297:−
5279:−
5155:−
5125:−
5111:−
5066:−
5048:−
4719:−
4683:∑
4672:λ
4494:−
4485:−
4473:−
4464:
4458:∼
4378:−
4369:−
4354:−
4330:
4266:
4260:⋅
4254:−
4197:−
4125:−
4066:
4060:⋅
4054:−
4029:
3998:
3970:−
3948:
3871:−
3812:
3774:−
3765:−
3753:−
3744:
3738:∼
3719:−
3667:−
3628:≥
3616:≥
3577:−
3396:⋯
3318:…
3265:…
2918:−
2902:−
2888:−
2864:−
2858:−
2842:−
2836:−
2822:−
2798:−
2783:−
2623:−
2606:−
2600:−
2591:⋅
2582:⋅
2574:−
2551:−
2533:−
2246:−
2224:
2218:∼
2163:−
2149:−
2135:−
2112:−
2094:−
1898:…
1765:…
1651:−
1642:−
1627:≤
1607:…
1581:
1479:≤
1459:…
1433:
1361:−
1331:−
1317:−
1253:−
1235:−
1152:−
1122:−
1042:∑
896:they are
596:−
557:…
471:…
417:) is the
364:…
79:inference
12649:Category
12342:Survival
12219:Johansen
11942:Binomial
11897:Isotonic
11484:(normal)
11129:location
10936:Blocking
10891:Sampling
10770:QâQ plot
10735:Box plot
10717:Graphics
10612:Skewness
10602:Kurtosis
10574:Variance
10504:Heronian
10499:Harmonic
10288:14334678
10201:(1946).
10179:: 9â18.
10136:(1953).
9877:Quartile
9862:Quantile
9803:Box plot
9792:See also
8207:Suppose
7173:″
6413:kurtosis
4595:from an
3209:constant
2996:, 1 and
838:, ..., X
12675:Commons
12622:Kriging
12507:Process
12464:studies
12323:Wavelet
12156:General
11323:Plug-in
11117:L space
10896:Cluster
10597:Moments
10415:Outline
9925:improve
8150:end for
7952:end for
7828:6:
7677:matrix
7590:2: Set
7532:1: Set
6390:Bahadur
6376:is the
6368:is the
1712:on the
907:, ...,
892:form a
883:, ...,
857:, ...,
821:, ...,
419:maximum
312:minimum
111:from a
90:maximum
86:minimum
12544:Census
12134:Normal
12082:Manova
11902:Robust
11652:2-way
11644:1-way
11482:-test
11153:
10730:Biplot
10521:Median
10514:Lehmer
10456:Center
10317:
10286:
10117:
10046:
10016:
9989:
9914:, but
9882:Median
9872:Decile
9798:Rankit
8429:
8192:kernel
8154:return
7277:, and
7230:where
6529:where
6493:
6472:
6372:, and
6364:where
5724:where
5531:where
4447:where
2670:, the
2654:+ 1).
894:sample
405:, the
240:
237:
209:
206:
178:
175:
115:, the
53:, the
12168:Trend
11697:prior
11639:anova
11528:-test
11502:-test
11494:-test
11401:Power
11346:Pivot
11139:shape
11134:scale
10584:Shape
10564:Range
10509:Heinz
10484:Cubic
10420:Index
10284:S2CID
10266:arXiv
8148:11:
7553:round
6645:with
6427:Proof
1790:is a
1716:have
850:) of
61:of a
12401:Test
11601:Sign
11453:Wald
10526:Mode
10464:Mean
10315:ISBN
10230:2015
10115:ISBN
10044:ISBN
10014:ISBN
9987:ISBN
9887:Mean
9784:log
9761:and
9298:<
8925:<
8870:<
8508:>
8387:<
8295:and
8190:and
8152:12:
6664:and
4919:and
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4529:For
4461:Beta
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2460:and
2328:and
2308:and
2221:Beta
1578:Prob
1430:Prob
760:and
715:even
506:The
306:(or
302:The
88:and
77:and
11581:BIC
11576:AIC
10339:at
10307:doi
10276:doi
10217:doi
10181:doi
10152:doi
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9788:).
7830:for
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7826:do
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