1346:-statistic", Section 5.7, pp. 199-201), 7 ("The distribution of the sample covariance matrix and the sample generalized variance", Section 7.9, pp. 242-248), 8 ("Testing the general linear hypothesis; multivariate analysis of variance", Section 8.11, pp. 370-374), 9 ("Testing independence of sets of variates", Section 9.11, pp. 404-408), 10 ("Testing hypotheses of equality of covariance matrices and equality of mean vectors and covariance vectors", Section 10.11, pp. 449-454), 11 ("Principal components", Section 11.8, pp. 482-483), 13 ("The distribution of characteristic roots and vectors", Section 13.8, pp. 563-567))
5497:
5483:
3187:
5521:
5509:
3197:
1342:, The final section of the text (before "Problems") that are always entitled "Elliptically contoured distributions", of the following chapters: Chapters 3 ("Estimation of the mean vector and the covariance matrix", Section 3.6, pp. 101-108), 4 ("The distributions and uses of sample correlation coefficients", Section 4.5, pp. 158-163), 5 ("The generalized
73:, or light (in comparison with the normal distribution). Some statistical methods that were originally motivated by the study of the normal distribution have good performance for general elliptical distributions (with finite variance), particularly for spherical distributions (which are defined below). Elliptical distributions are also used in
1111:
because, if the returns on all assets available for portfolio formation are jointly elliptically distributed, then all portfolios can be characterized completely by their location and scale – that is, any two portfolios with identical location and scale of portfolio return have identical
1095:, in which researchers examine how statistical procedures perform on the class of elliptical distributions, to gain insight into the procedures' performance on even more general problems, for example by using the
435:
230:
789:
725:
1033:
549:
279:
844:
906:
299:
135:
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653:
529:
256:
1053:
864:
809:
745:
502:
482:
458:
159:
107:
1845:
993:, in which most methods for estimation and hypothesis-testing are motivated for the normal distribution. In contrast to classical multivariate analysis,
1000:
For suitable elliptical distributions, some classical methods continue to have good properties. Under finite-variance assumptions, an extension of
1059:. For spherical distributions, classical results on parameter-estimation and hypothesis-testing hold have been extended. Similar results hold for
1706:
Owen, Joel; Rabinovitch, Ramon (June 1983). "On the Class of
Elliptical Distributions and their Applications to the Theory of Portfolio Choice".
4618:
5123:
86:
5547:
5273:
1974:
4897:
3538:
3200:
2457:
2365:
4671:
3152:
345:
5110:
3018:
2230:
1989:
1838:
2913:
2677:
2351:
1696:
1655:
3533:
3233:
2672:
2616:
2514:
2276:
1914:
1275:
Schmidt, Rafael (2012). "Credit Risk
Modeling and Estimation via Elliptical Copulae". In Bol, George; et al. (eds.).
918:
of each other (the mean of each subvector conditional on the value of the other subvector equals the unconditional mean).
4137:
3285:
2958:
2692:
2545:
2220:
1964:
1556:
Chamberlain, Gary (February 1983). "A characterization of the distributions that imply meanâVariance utility functions".
167:
2422:
3190:
2862:
2838:
2417:
1831:
595:
4920:
4812:
3059:
2936:
2897:
2869:
2843:
2761:
2687:
2110:
1858:
1761:
1620:
1519:
1284:
590:
5557:
5525:
5098:
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3047:
3013:
2879:
2874:
2719:
2527:
2225:
1979:
979:
671:
585:
571:
36:
667:. All these ellipsoids or ellipses have the common center μ and are scaled copies (homothets) of each other.
5156:
4817:
4562:
3933:
3523:
2797:
2710:
2682:
2591:
2540:
2412:
2195:
2160:
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2811:
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2312:
2190:
2165:
2029:
2024:
2019:
1804:
1675:
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1463:
1113:
1096:
4147:
1167:
Multivariate statistical simulation: A guide to selecting and generating continuous multivariate distributions
5450:
4409:
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3127:
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2701:
2550:
2482:
2467:
2360:
2334:
2266:
2105:
1999:
1994:
1936:
1921:
1219:
Pascal, F.; et al. (2013). "Parameter
Estimation For Multivariate Generalized Gaussian Distributions".
5562:
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4414:
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2130:
997:
multivariate analysis refers to research on elliptical distributions without the restriction of normality.
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3142:
2918:
2737:
2519:
2472:
2341:
2317:
2297:
2140:
2014:
1894:
953:
Elliptical distributions are used in statistics and in economics. They are also used to calculate the
4962:
4730:
4451:
4376:
4305:
4234:
4154:
4142:
4012:
4000:
3993:
3701:
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2392:
2290:
2254:
2125:
2090:
1184:
Frahm, G., Junker, M., & Szimayer, A. (2003). Elliptical copulas: Applicability and limitations.
1064:
811:), in general elliptical distributions can be bounded or unboundedâsuch a distribution is bounded if
5445:
5212:
5075:
4760:
4725:
4689:
4474:
3916:
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3784:
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2120:
2009:
1904:
1854:
750:
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552:
32:
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2200:
2150:
2145:
1946:
1926:
601:
39:. Intuitively, in the simplified two and three dimensional case, the joint distribution forms an
2302:
941:
is elliptical (though not necessarily with the same elliptical distribution), and any subset of
659:
or a union of ellipses (hence the name elliptical distribution). More generally, for arbitrary
5392:
5322:
5115:
5052:
4807:
4694:
3691:
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3495:
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2998:
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2004:
1984:
1889:
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882:
306:
1015:
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5359:
5302:
5128:
5021:
4930:
4656:
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4088:
3984:
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3079:
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1899:
990:
747:
can take on arbitrarily large positive or negative values with non-zero probability, because
534:
264:
58:
1615:. Monographs on statistics and applied probability. Vol. 36. London: Chapman and Hall.
814:
305:
random-vectors has been extended to accommodate random vectors in
Euclidean spaces over the
5340:
4915:
4864:
4840:
4802:
4720:
4699:
4651:
4530:
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1507:
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1001:
965:
888:
461:
318:
314:
284:
120:
2377:
1670:. Mathematics and Its Applications (1st ed.). Dordrecht: Kluwer Academic Publishers.
629:
514:
241:
8:
5487:
5412:
5335:
5016:
4780:
4773:
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3392:
3317:
3219:
3106:
2631:
2611:
2581:
2555:
2509:
2437:
2249:
2185:
1748:. Springer series in statistics. Science Press (Beijing) and Springer-Verlag (New York).
1068:
874:
325:
138:
1242:
5501:
5312:
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5062:
5011:
4887:
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4239:
4199:
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4005:
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3137:
2626:
2407:
2402:
2307:
2244:
2239:
2095:
2085:
1969:
1723:
1254:
1228:
1200:"Multivariate stable densities and distribution functions: general and elliptical case"
1038:
849:
794:
730:
487:
467:
443:
322:
236:
144:
92:
5496:
5407:
5377:
5369:
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5105:
5036:
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4852:
4740:
4681:
4547:
4535:
4161:
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4022:
3945:
3789:
3711:
3490:
3364:
3035:
2462:
2205:
2135:
2100:
2049:
1810:
1800:
1767:
1757:
1692:
1671:
1651:
1626:
1616:
1592:
1582:
1569:
1547:
1530:
1515:
1459:
1280:
1199:
1112:
distributions of portfolio return. Various features of portfolio analysis, including
1092:
1072:
954:
612:
In the 2-dimensional case, if the density exists, each iso-density locus (the set of
556:
74:
65:
multivariate analysis, for the study of symmetric distributions with tails that are
5432:
5387:
5151:
5138:
5031:
5006:
4940:
4872:
4750:
4358:
4251:
4184:
4097:
4044:
3863:
3734:
3528:
3412:
3327:
3294:
2210:
1884:
1823:
1749:
1715:
1643:
1565:
1542:
1258:
1246:
1108:
961:
915:
509:
332:
5349:
5093:
4955:
4882:
4557:
4431:
4404:
4381:
4350:
3977:
3972:
3926:
3656:
3307:
1372:, Chapter 2.8 "Distribution of quadratic forms and Cochran's theorem", pp. 74-81)
1080:
110:
4839:
5298:
5293:
3756:
3686:
3332:
2283:
960:
In mathematical economics, elliptical distributions have been used to describe
310:
1753:
1647:
5541:
5455:
5422:
5285:
5246:
5057:
5026:
4490:
4444:
4049:
3751:
3578:
3342:
3337:
2906:
2654:
1941:
1630:
1596:
1250:
505:
1814:
1771:
881:
enters the density function quadratically, all elliptical distributions are
16:
Family of distributions that generalize the multivariate normal distribution
5397:
5330:
5307:
5222:
4552:
3848:
3746:
3681:
3623:
3608:
3545:
3500:
1788:
1604:
911:
331:
Some elliptical distributions are alternatively defined in terms of their
5440:
5402:
5085:
4986:
4848:
4661:
4628:
4120:
4037:
4032:
3676:
3633:
3613:
3593:
3583:
3352:
1797:
Statistical inference in elliptically contoured and related distributions
1736:
1608:
20:
1151:, Chapter 2.9 "Complex elliptically symmetric distributions", pp. 64-66)
567:
Examples include the following multivariate probability distributions:
4286:
3766:
3466:
3397:
3347:
3322:
3242:
1727:
66:
51:
24:
4439:
4291:
3911:
3706:
3618:
3603:
3598:
3563:
1012:
An elliptical distribution with a zero mean and variance in the form
664:
44:
1719:
3955:
3573:
3450:
3445:
3440:
1163:, Chapter 6, "Elliptically contoured distributions, pp. 106-124):
934:
1233:
5460:
5161:
656:
40:
1640:
Elliptically contoured models in statistics and portfolio theory
971:
5382:
4363:
4337:
4317:
3568:
3359:
727:. While the multivariate normal is unbounded (each element of
3211:
1063:, and indeed also for complicated models (especially for the
430:{\displaystyle f(x)=k\cdot g((x-\mu )'\Sigma ^{-1}(x-\mu ))}
3302:
870:
531:(which is also the mean vector if the latter exists), and
77:
to evaluate proposed multivariate-statistical procedures.
1529:
Cambanis, Stamatis; Huang, Steel; Simons, Gordon (1981).
910:
If two subsets of a jointly elliptical random vector are
869:
There exist elliptical distributions that have undefined
1581:. Science Press (Beijing) and Springer-Verlag (Berlin).
1531:"On the theory of elliptically contoured distributions"
335:. An elliptical distribution with a density function
1638:
Gupta, Arjun K.; Varga, Tamas; Bodnar, Taras (2013).
1396:, Chapter IV "Estimation of parameters", pp. 127-153)
1041:
1018:
891:
852:
817:
797:
753:
733:
680:
632:
537:
517:
490:
470:
446:
348:
317:. Computational methods are available for generating
287:
267:
244:
170:
147:
123:
95:
85:
Elliptical distributions are defined in terms of the
5124:
Autoregressive conditional heteroskedasticity (ARCH)
1853:
1512:
An introduction to multivariate statistical analysis
877:(even in the univariate case). Because the variable
1611:; Ng, Kai Wang ("Kai-Wang" on front cover) (1990).
1528:
1387:
1384:, Chapter 2.5 "Spherical distributions", pp. 53-64)
1277:
Credit Risk: Measurement, Evaluation and
Management
1136:
937:. Thus any linear combination of the components of
225:{\displaystyle \phi _{X-\mu }(t)=\psi (t'\Sigma t)}
4586:
1375:
1333:
1047:
1027:
900:
858:
838:
803:
783:
739:
719:
647:
543:
523:
496:
476:
452:
429:
321:vectors from elliptical distributions, for use in
293:
273:
250:
224:
153:
129:
101:
1435:
1086:
1067:model). The analysis of multivariate models uses
301:. The definition of elliptical distributions for
5539:
1637:
1613:Symmetric multivariate and related distributions
1472:
1399:
1363:
1318:
1004:(on the distribution of quadratic forms) holds.
5553:Location-scale family probability distributions
4672:Multivariate adaptive regression splines (MARS)
1742:Growth curve models and statistical diagnostics
1705:
1514:(3rd ed.). New York: John Wiley and Sons.
1411:
1306:
1274:
1171:, "an admirably lucid discussion" according to
1689:Advanced multivariate statistics with matrices
1686:
1478:
1441:
1408:, Chapter V "Testing hypotheses", pp. 154-187)
1091:Another use of elliptical distributions is in
3227:
1839:
1330:(Chamberlain 1983; Owen and Rabinovitch 1983)
972:Statistics: Generalized multivariate analysis
61:, while elliptical distributions are used in
1787:
1354:
1352:
1668:Elliptically contoured models in statistics
1642:(2nd ed.). New York: Springer-Verlag.
1555:
1490:
1453:
1447:
1420:, Chapter VII "Linear models", pp. 188-211)
1302:
1300:
1298:
1296:
1197:
591:Symmetric multivariate Laplace distribution
3272:
3234:
3220:
1846:
1832:
1665:
1603:
1218:
1172:
1148:
1107:Elliptical distributions are important in
586:Symmetric multivariate stable distribution
3885:
1687:Kollo, TÔnu; von Rosen, Dietrich (2005).
1576:
1546:
1454:Kariya, Takeaki; Sinha, Bimal K. (1989).
1417:
1405:
1393:
1381:
1369:
1358:
1349:
1270:
1268:
1232:
1120:, hold for all elliptical distributions.
1007:
1506:
1339:
1293:
1102:
925:is elliptically distributed, then so is
1734:
1577:Fang, Kai-Tai; Zhang, Yao-Ting (1990).
1429:
1423:
1164:
1160:
626:pairs all giving a particular value of
89:of probability theory. A random vector
5540:
5198:KaplanâMeier estimator (product limit)
1666:Gupta, Arjun K.; Varga, Tamas (1993).
1265:
1221:IEEE Transactions on Signal Processing
47:, respectively, in iso-density plots.
5271:
4838:
4585:
3884:
3654:
3271:
3215:
1827:
914:, then if their means exist they are
663:, the iso-density loci are unions of
54:, the normal distribution is used in
5508:
5208:Accelerated failure time (AFT) model
3196:
1186:Statistics & Probability Letters
5520:
4803:Analysis of variance (ANOVA, anova)
3655:
1055:is the identity-matrix is called a
31:is any member of a broad family of
13:
5548:Types of probability distributions
4898:CochranâMantelâHaenszel statistics
3524:Pearson product-moment correlation
1780:
1198:Nolan, John (September 29, 2014).
1137:Cambanis, Huang & Simons (1981
1130:
596:Multivariate logistic distribution
538:
397:
313:, so facilitating applications in
268:
213:
14:
5574:
1579:Generalized multivariate analysis
5519:
5507:
5495:
5482:
5481:
5272:
3195:
3186:
3185:
1535:Journal of Multivariate Analysis
672:multivariate normal distribution
572:Multivariate normal distribution
37:multivariate normal distribution
5157:Least-squares spectral analysis
1484:
1456:Robustness of statistical tests
1324:
1114:mutual fund separation theorems
948:
600:Multivariate symmetric general
117:if its characteristic function
4138:Mean-unbiased minimum-variance
3241:
1319:Gupta, Varga & Bodnar 2013
1311:
1212:
1191:
1178:
1154:
1142:
1087:Robust statistics: Asymptotics
827:
821:
690:
684:
642:
636:
424:
421:
409:
389:
376:
373:
358:
352:
219:
202:
193:
187:
1:
5451:Geographic information system
4667:Simultaneous equations models
1499:
1307:Owen & Rabinovitch (1983)
1097:limiting theory of statistics
784:{\displaystyle e^{-z/2}>0}
720:{\displaystyle g(z)=e^{-z/2}}
674:is the special case in which
607:
555:which is proportional to the
80:
4634:Coefficient of determination
4245:Uniformly most powerful test
1799:. New York: Allerton Press.
1570:10.1016/0022-0531(83)90129-1
1548:10.1016/0047-259x(81)90082-8
7:
5203:Proportional hazards models
5147:Spectral density estimation
5129:Vector autoregression (VAR)
4563:Maximum posterior estimator
3795:Randomized controlled trial
1479:Kollo & von Rosen (2005
1442:Kollo & von Rosen (2005
1118:Capital Asset Pricing Model
562:
260:nonnegative-definite matrix
71:multivariate t-distribution
10:
5579:
4963:Multivariate distributions
3383:Average absolute deviation
3019:Wrapped asymmetric Laplace
1990:Extended negative binomial
1558:Journal of Economic Theory
281:and some scalar function
5477:
5431:
5368:
5321:
5284:
5280:
5267:
5239:
5221:
5188:
5179:
5137:
5084:
5045:
4994:
4985:
4951:Structural equation model
4906:
4863:
4859:
4834:
4793:
4759:
4713:
4680:
4642:
4609:
4605:
4581:
4521:
4430:
4349:
4313:
4304:
4287:Score/Lagrange multiplier
4272:
4225:
4170:
4096:
4087:
3897:
3893:
3880:
3839:
3813:
3765:
3720:
3702:Sample size determination
3667:
3663:
3650:
3554:
3509:
3483:
3465:
3421:
3373:
3293:
3284:
3280:
3267:
3249:
3181:
3115:
3073:
2974:
2810:
2788:
2779:
2678:Generalized extreme value
2663:
2498:
2458:Relativistic BreitâWigner
2174:
2071:
2062:
1955:
1875:
1866:
1855:Probability distributions
1754:10.1007/978-0-387-21812-0
1648:10.1007/978-1-4614-8154-6
1279:. Springer. p. 274.
1173:Fang, Kotz & Ng (1990
1165:Johnson, Mark E. (1987).
1149:Fang, Kotz & Ng (1990
866:greater than some value.
141:(for every column-vector
33:probability distributions
5446:Environmental statistics
4968:Elliptical distributions
4761:Generalized linear model
4690:Simple linear regression
4460:HodgesâLehmann estimator
3917:Probability distribution
3826:Stochastic approximation
3388:Coefficient of variation
1251:10.1109/TSP.2013.2282909
1123:
1028:{\displaystyle \alpha I}
553:positive definite matrix
137:satisfies the following
5558:Multivariate statistics
5106:Cross-correlation (XCF)
4714:Non-standard predictors
4148:LehmannâScheffĂ© theorem
3821:Adaptive clinical trial
2673:Generalized chi-squared
2617:Normal-inverse Gaussian
1819:A collection of papers.
1691:. Dordrecht: Springer.
1359:Fang & Zhang (1990)
602:hyperbolic distribution
544:{\displaystyle \Sigma }
274:{\displaystyle \Sigma }
115:elliptical distribution
87:characteristic function
29:elliptical distribution
5502:Mathematics portal
5323:Engineering statistics
5231:NelsonâAalen estimator
4808:Analysis of covariance
4695:Ordinary least squares
4619:Pearson product-moment
4023:Statistical functional
3934:Empirical distribution
3767:Controlled experiments
3496:Frequency distribution
3274:Descriptive statistics
2985:Univariate (circular)
2546:Generalized hyperbolic
1975:ConwayâMaxwellâPoisson
1965:Beta negative binomial
1708:The Journal of Finance
1418:Fang & Zhang (1990
1406:Fang & Zhang (1990
1394:Fang & Zhang (1990
1382:Fang & Zhang (1990
1370:Fang & Zhang (1990
1169:. John Wiley and Sons.
1057:spherical distribution
1049:
1029:
1008:Spherical distribution
986:(of Gauss) is used in
902:
860:
840:
839:{\displaystyle g(z)=0}
805:
785:
741:
721:
649:
559:if the latter exists.
545:
525:
498:
478:
454:
431:
295:
275:
252:
226:
155:
131:
103:
5418:Population statistics
5360:System identification
5094:Autocorrelation (ACF)
5022:Exponential smoothing
4936:Discriminant analysis
4931:Canonical correlation
4795:Partition of variance
4657:Regression validation
4501:(JonckheereâTerpstra)
4400:Likelihood-ratio test
4089:Frequentist inference
4001:Locationâscale family
3922:Sampling distribution
3887:Statistical inference
3854:Cross-sectional study
3841:Observational studies
3800:Randomized experiment
3629:Stem-and-leaf display
3431:Central limit theorem
3030:Bivariate (spherical)
2528:Kaniadakis Îș-Gaussian
1103:Economics and finance
1050:
1030:
991:multivariate analysis
903:
901:{\displaystyle \mu .}
861:
841:
806:
791:for all non-negative
786:
742:
722:
650:
546:
526:
499:
479:
455:
432:
296:
294:{\displaystyle \psi }
276:
253:
227:
156:
132:
130:{\displaystyle \phi }
104:
59:multivariate analysis
5341:Probabilistic design
4926:Principal components
4769:Exponential families
4721:Nonlinear regression
4700:General linear model
4662:Mixed effects models
4652:Errors and residuals
4629:Confounding variable
4531:Bayesian probability
4509:Van der Waerden test
4499:Ordered alternative
4264:Multiple comparisons
4143:RaoâBlackwellization
4106:Estimating equations
4062:Statistical distance
3780:Factorial experiment
3313:Arithmetic-Geometric
3095:Dirac delta function
3042:Bivariate (toroidal)
2999:Univariate von Mises
2870:Multivariate Laplace
2762:Shifted log-logistic
2111:Continuous Bernoulli
1430:Pan & Fang (2007
1039:
1016:
966:mathematical finance
889:
850:
815:
795:
751:
731:
678:
648:{\displaystyle f(x)}
630:
535:
524:{\displaystyle \mu }
515:
488:
468:
462:normalizing constant
444:
346:
315:time-series analysis
285:
265:
251:{\displaystyle \mu }
242:
168:
145:
121:
93:
35:that generalize the
5563:Normal distribution
5413:Official statistics
5336:Methods engineering
5017:Seasonal adjustment
4785:Poisson regressions
4705:Bayesian regression
4644:Regression analysis
4624:Partial correlation
4596:Regression analysis
4195:Prediction interval
4190:Likelihood interval
4180:Confidence interval
4172:Interval estimation
4133:Unbiased estimators
3951:Model specification
3831:Up-and-down designs
3519:Partial correlation
3475:Index of dispersion
3393:Interquartile range
3143:Natural exponential
3048:Bivariate von Mises
3014:Wrapped exponential
2880:Multivariate stable
2875:Multivariate normal
2196:Benktander 2nd kind
2191:Benktander 1st kind
1980:Discrete phase-type
1243:2013ITSP...61.5960P
1069:multilinear algebra
978:In statistics, the
875:Cauchy distribution
139:functional equation
5433:Spatial statistics
5313:Medical statistics
5213:First hitting time
5167:Whittle likelihood
4818:Degrees of freedom
4813:Multivariate ANOVA
4746:Heteroscedasticity
4558:Bayesian estimator
4523:Bayesian inference
4372:KolmogorovâSmirnov
4257:Randomization test
4227:Testing hypotheses
4200:Tolerance interval
4111:Maximum likelihood
4006:Exponential family
3939:Density estimation
3899:Statistical theory
3859:Natural experiment
3805:Scientific control
3722:Survey methodology
3408:Standard deviation
2798:Rectified Gaussian
2683:Generalized Pareto
2541:Generalized normal
2413:Matrix-exponential
1491:Chamberlain (1983)
1458:. Academic Press.
1073:Kronecker products
1045:
1025:
955:landing footprints
898:
856:
836:
801:
781:
737:
717:
645:
541:
521:
494:
474:
450:
427:
291:
271:
248:
237:location parameter
222:
151:
127:
99:
5535:
5534:
5473:
5472:
5469:
5468:
5408:National accounts
5378:Actuarial science
5370:Social statistics
5263:
5262:
5259:
5258:
5255:
5254:
5190:Survival function
5175:
5174:
5037:Granger causality
4878:Contingency table
4853:Survival analysis
4830:
4829:
4826:
4825:
4682:Linear regression
4577:
4576:
4573:
4572:
4548:Credible interval
4517:
4516:
4300:
4299:
4116:Method of moments
3985:Parametric family
3946:Statistical model
3876:
3875:
3872:
3871:
3790:Random assignment
3712:Statistical power
3646:
3645:
3642:
3641:
3491:Contingency table
3461:
3460:
3328:Generalized/power
3209:
3208:
2806:
2805:
2775:
2774:
2666:whose type varies
2612:Normal (Gaussian)
2566:Hyperbolic secant
2515:Exponential power
2418:MaxwellâBoltzmann
2166:Wigner semicircle
2058:
2057:
2030:Parabolic fractal
2020:Negative binomial
1698:978-1-4020-3418-3
1657:978-1-4614-8153-9
1227:(23): 5960â5971.
1188:, 63(3), 275â286.
1099:("asymptotics").
1093:robust statistics
1048:{\displaystyle I}
1002:Cochran's theorem
921:If random vector
859:{\displaystyle z}
804:{\displaystyle z}
740:{\displaystyle x}
557:covariance matrix
497:{\displaystyle n}
477:{\displaystyle x}
453:{\displaystyle k}
333:density functions
154:{\displaystyle t}
102:{\displaystyle X}
75:robust statistics
5570:
5523:
5522:
5511:
5510:
5500:
5499:
5485:
5484:
5388:Crime statistics
5282:
5281:
5269:
5268:
5186:
5185:
5152:Fourier analysis
5139:Frequency domain
5119:
5066:
5032:Structural break
4992:
4991:
4941:Cluster analysis
4888:Log-linear model
4861:
4860:
4836:
4835:
4777:
4751:Homoscedasticity
4607:
4606:
4583:
4582:
4502:
4494:
4486:
4485:(KruskalâWallis)
4470:
4455:
4410:Cross validation
4395:
4377:AndersonâDarling
4324:
4311:
4310:
4282:Likelihood-ratio
4274:Parametric tests
4252:Permutation test
4235:1- & 2-tails
4126:Minimum distance
4098:Point estimation
4094:
4093:
4045:Optimal decision
3996:
3895:
3894:
3882:
3881:
3864:Quasi-experiment
3814:Adaptive designs
3665:
3664:
3652:
3651:
3529:Rank correlation
3291:
3290:
3282:
3281:
3269:
3268:
3236:
3229:
3222:
3213:
3212:
3199:
3198:
3189:
3188:
3128:Compound Poisson
3103:
3091:
3060:von MisesâFisher
3056:
3044:
3032:
2994:Circular uniform
2990:
2910:
2854:
2825:
2786:
2785:
2688:MarchenkoâPastur
2551:Geometric stable
2468:Truncated normal
2361:Inverse Gaussian
2267:Hyperexponential
2106:Beta rectangular
2074:bounded interval
2069:
2068:
1937:Discrete uniform
1922:Poisson binomial
1873:
1872:
1848:
1841:
1834:
1825:
1824:
1818:
1775:
1747:
1731:
1702:
1681:
1661:
1634:
1600:
1573:
1552:
1550:
1525:
1493:
1488:
1482:
1476:
1470:
1469:
1451:
1445:
1439:
1433:
1427:
1421:
1415:
1409:
1403:
1397:
1391:
1385:
1379:
1373:
1367:
1361:
1356:
1347:
1337:
1331:
1328:
1322:
1315:
1309:
1304:
1291:
1290:
1272:
1263:
1262:
1236:
1216:
1210:
1209:
1207:
1206:
1195:
1189:
1182:
1176:
1170:
1158:
1152:
1146:
1140:
1134:
1109:portfolio theory
1054:
1052:
1051:
1046:
1034:
1032:
1031:
1026:
916:mean independent
907:
905:
904:
899:
865:
863:
862:
857:
845:
843:
842:
837:
810:
808:
807:
802:
790:
788:
787:
782:
774:
773:
769:
746:
744:
743:
738:
726:
724:
723:
718:
716:
715:
711:
654:
652:
651:
646:
550:
548:
547:
542:
530:
528:
527:
522:
503:
501:
500:
495:
483:
481:
480:
475:
459:
457:
456:
451:
436:
434:
433:
428:
408:
407:
395:
300:
298:
297:
292:
280:
278:
277:
272:
257:
255:
254:
249:
231:
229:
228:
223:
212:
186:
185:
160:
158:
157:
152:
136:
134:
133:
128:
108:
106:
105:
100:
5578:
5577:
5573:
5572:
5571:
5569:
5568:
5567:
5538:
5537:
5536:
5531:
5494:
5465:
5427:
5364:
5350:quality control
5317:
5299:Clinical trials
5276:
5251:
5235:
5223:Hazard function
5217:
5171:
5133:
5117:
5080:
5076:BreuschâGodfrey
5064:
5041:
4981:
4956:Factor analysis
4902:
4883:Graphical model
4855:
4822:
4789:
4775:
4755:
4709:
4676:
4638:
4601:
4600:
4569:
4513:
4500:
4492:
4484:
4468:
4453:
4432:Rank statistics
4426:
4405:Model selection
4393:
4351:Goodness of fit
4345:
4322:
4296:
4268:
4221:
4166:
4155:Median unbiased
4083:
3994:
3927:Order statistic
3889:
3868:
3835:
3809:
3761:
3716:
3659:
3657:Data collection
3638:
3550:
3505:
3479:
3457:
3417:
3369:
3286:Continuous data
3276:
3263:
3245:
3240:
3210:
3205:
3177:
3153:Maximum entropy
3111:
3099:
3087:
3077:
3069:
3052:
3040:
3028:
2983:
2970:
2907:Matrix-valued:
2904:
2850:
2821:
2813:
2802:
2790:
2781:
2771:
2665:
2659:
2576:
2502:
2500:
2494:
2423:MaxwellâJĂŒttner
2272:Hypoexponential
2178:
2176:
2175:supported on a
2170:
2131:Noncentral beta
2091:BaldingâNichols
2073:
2072:supported on a
2064:
2054:
1957:
1951:
1947:ZipfâMandelbrot
1877:
1868:
1862:
1852:
1822:
1807:
1795:, eds. (1990).
1793:Anderson, T. W.
1783:
1781:Further reading
1778:
1764:
1745:
1720:10.2307/2328079
1699:
1678:
1658:
1623:
1589:
1522:
1508:Anderson, T. W.
1502:
1497:
1496:
1489:
1485:
1477:
1473:
1466:
1452:
1448:
1444:, p. xiii)
1440:
1436:
1428:
1424:
1416:
1412:
1404:
1400:
1392:
1388:
1380:
1376:
1368:
1364:
1357:
1350:
1338:
1334:
1329:
1325:
1316:
1312:
1305:
1294:
1287:
1273:
1266:
1217:
1213:
1204:
1202:
1196:
1192:
1183:
1179:
1159:
1155:
1147:
1143:
1135:
1131:
1126:
1105:
1089:
1081:matrix calculus
1040:
1037:
1036:
1017:
1014:
1013:
1010:
974:
957:of spacecraft.
951:
945:is elliptical.
929:for any matrix
890:
887:
886:
851:
848:
847:
816:
813:
812:
796:
793:
792:
765:
758:
754:
752:
749:
748:
732:
729:
728:
707:
700:
696:
679:
676:
675:
631:
628:
627:
625:
618:
610:
565:
536:
533:
532:
516:
513:
512:
489:
486:
485:
469:
466:
465:
445:
442:
441:
400:
396:
388:
347:
344:
343:
311:complex numbers
286:
283:
282:
266:
263:
262:
243:
240:
239:
205:
175:
171:
169:
166:
165:
146:
143:
142:
122:
119:
118:
111:Euclidean space
94:
91:
90:
83:
17:
12:
11:
5:
5576:
5566:
5565:
5560:
5555:
5550:
5533:
5532:
5530:
5529:
5517:
5505:
5491:
5478:
5475:
5474:
5471:
5470:
5467:
5466:
5464:
5463:
5458:
5453:
5448:
5443:
5437:
5435:
5429:
5428:
5426:
5425:
5420:
5415:
5410:
5405:
5400:
5395:
5390:
5385:
5380:
5374:
5372:
5366:
5365:
5363:
5362:
5357:
5352:
5343:
5338:
5333:
5327:
5325:
5319:
5318:
5316:
5315:
5310:
5305:
5296:
5294:Bioinformatics
5290:
5288:
5278:
5277:
5265:
5264:
5261:
5260:
5257:
5256:
5253:
5252:
5250:
5249:
5243:
5241:
5237:
5236:
5234:
5233:
5227:
5225:
5219:
5218:
5216:
5215:
5210:
5205:
5200:
5194:
5192:
5183:
5177:
5176:
5173:
5172:
5170:
5169:
5164:
5159:
5154:
5149:
5143:
5141:
5135:
5134:
5132:
5131:
5126:
5121:
5113:
5108:
5103:
5102:
5101:
5099:partial (PACF)
5090:
5088:
5082:
5081:
5079:
5078:
5073:
5068:
5060:
5055:
5049:
5047:
5046:Specific tests
5043:
5042:
5040:
5039:
5034:
5029:
5024:
5019:
5014:
5009:
5004:
4998:
4996:
4989:
4983:
4982:
4980:
4979:
4978:
4977:
4976:
4975:
4960:
4959:
4958:
4948:
4946:Classification
4943:
4938:
4933:
4928:
4923:
4918:
4912:
4910:
4904:
4903:
4901:
4900:
4895:
4893:McNemar's test
4890:
4885:
4880:
4875:
4869:
4867:
4857:
4856:
4832:
4831:
4828:
4827:
4824:
4823:
4821:
4820:
4815:
4810:
4805:
4799:
4797:
4791:
4790:
4788:
4787:
4771:
4765:
4763:
4757:
4756:
4754:
4753:
4748:
4743:
4738:
4733:
4731:Semiparametric
4728:
4723:
4717:
4715:
4711:
4710:
4708:
4707:
4702:
4697:
4692:
4686:
4684:
4678:
4677:
4675:
4674:
4669:
4664:
4659:
4654:
4648:
4646:
4640:
4639:
4637:
4636:
4631:
4626:
4621:
4615:
4613:
4603:
4602:
4599:
4598:
4593:
4587:
4579:
4578:
4575:
4574:
4571:
4570:
4568:
4567:
4566:
4565:
4555:
4550:
4545:
4544:
4543:
4538:
4527:
4525:
4519:
4518:
4515:
4514:
4512:
4511:
4506:
4505:
4504:
4496:
4488:
4472:
4469:(MannâWhitney)
4464:
4463:
4462:
4449:
4448:
4447:
4436:
4434:
4428:
4427:
4425:
4424:
4423:
4422:
4417:
4412:
4402:
4397:
4394:(ShapiroâWilk)
4389:
4384:
4379:
4374:
4369:
4361:
4355:
4353:
4347:
4346:
4344:
4343:
4335:
4326:
4314:
4308:
4306:Specific tests
4302:
4301:
4298:
4297:
4295:
4294:
4289:
4284:
4278:
4276:
4270:
4269:
4267:
4266:
4261:
4260:
4259:
4249:
4248:
4247:
4237:
4231:
4229:
4223:
4222:
4220:
4219:
4218:
4217:
4212:
4202:
4197:
4192:
4187:
4182:
4176:
4174:
4168:
4167:
4165:
4164:
4159:
4158:
4157:
4152:
4151:
4150:
4145:
4130:
4129:
4128:
4123:
4118:
4113:
4102:
4100:
4091:
4085:
4084:
4082:
4081:
4076:
4071:
4070:
4069:
4059:
4054:
4053:
4052:
4042:
4041:
4040:
4035:
4030:
4020:
4015:
4010:
4009:
4008:
4003:
3998:
3982:
3981:
3980:
3975:
3970:
3960:
3959:
3958:
3953:
3943:
3942:
3941:
3931:
3930:
3929:
3919:
3914:
3909:
3903:
3901:
3891:
3890:
3878:
3877:
3874:
3873:
3870:
3869:
3867:
3866:
3861:
3856:
3851:
3845:
3843:
3837:
3836:
3834:
3833:
3828:
3823:
3817:
3815:
3811:
3810:
3808:
3807:
3802:
3797:
3792:
3787:
3782:
3777:
3771:
3769:
3763:
3762:
3760:
3759:
3757:Standard error
3754:
3749:
3744:
3743:
3742:
3737:
3726:
3724:
3718:
3717:
3715:
3714:
3709:
3704:
3699:
3694:
3689:
3687:Optimal design
3684:
3679:
3673:
3671:
3661:
3660:
3648:
3647:
3644:
3643:
3640:
3639:
3637:
3636:
3631:
3626:
3621:
3616:
3611:
3606:
3601:
3596:
3591:
3586:
3581:
3576:
3571:
3566:
3560:
3558:
3552:
3551:
3549:
3548:
3543:
3542:
3541:
3536:
3526:
3521:
3515:
3513:
3507:
3506:
3504:
3503:
3498:
3493:
3487:
3485:
3484:Summary tables
3481:
3480:
3478:
3477:
3471:
3469:
3463:
3462:
3459:
3458:
3456:
3455:
3454:
3453:
3448:
3443:
3433:
3427:
3425:
3419:
3418:
3416:
3415:
3410:
3405:
3400:
3395:
3390:
3385:
3379:
3377:
3371:
3370:
3368:
3367:
3362:
3357:
3356:
3355:
3350:
3345:
3340:
3335:
3330:
3325:
3320:
3318:Contraharmonic
3315:
3310:
3299:
3297:
3288:
3278:
3277:
3265:
3264:
3262:
3261:
3256:
3250:
3247:
3246:
3239:
3238:
3231:
3224:
3216:
3207:
3206:
3204:
3203:
3193:
3182:
3179:
3178:
3176:
3175:
3170:
3165:
3160:
3155:
3150:
3148:Locationâscale
3145:
3140:
3135:
3130:
3125:
3119:
3117:
3113:
3112:
3110:
3109:
3104:
3097:
3092:
3084:
3082:
3071:
3070:
3068:
3067:
3062:
3057:
3050:
3045:
3038:
3033:
3026:
3021:
3016:
3011:
3009:Wrapped Cauchy
3006:
3004:Wrapped normal
3001:
2996:
2991:
2980:
2978:
2972:
2971:
2969:
2968:
2967:
2966:
2961:
2959:Normal-inverse
2956:
2951:
2941:
2940:
2939:
2929:
2921:
2916:
2911:
2902:
2901:
2900:
2890:
2882:
2877:
2872:
2867:
2866:
2865:
2855:
2848:
2847:
2846:
2841:
2831:
2826:
2818:
2816:
2808:
2807:
2804:
2803:
2801:
2800:
2794:
2792:
2783:
2777:
2776:
2773:
2772:
2770:
2769:
2764:
2759:
2751:
2743:
2735:
2726:
2717:
2708:
2699:
2690:
2685:
2680:
2675:
2669:
2667:
2661:
2660:
2658:
2657:
2652:
2650:Variance-gamma
2647:
2642:
2634:
2629:
2624:
2619:
2614:
2609:
2601:
2596:
2595:
2594:
2584:
2579:
2574:
2568:
2563:
2558:
2553:
2548:
2543:
2538:
2530:
2525:
2517:
2512:
2506:
2504:
2496:
2495:
2493:
2492:
2490:Wilks's lambda
2487:
2486:
2485:
2475:
2470:
2465:
2460:
2455:
2450:
2445:
2440:
2435:
2430:
2428:Mittag-Leffler
2425:
2420:
2415:
2410:
2405:
2400:
2395:
2390:
2385:
2380:
2375:
2370:
2369:
2368:
2358:
2349:
2344:
2339:
2338:
2337:
2327:
2325:gamma/Gompertz
2322:
2321:
2320:
2315:
2305:
2300:
2295:
2294:
2293:
2281:
2280:
2279:
2274:
2269:
2259:
2258:
2257:
2247:
2242:
2237:
2236:
2235:
2234:
2233:
2223:
2213:
2208:
2203:
2198:
2193:
2188:
2182:
2180:
2177:semi-infinite
2172:
2171:
2169:
2168:
2163:
2158:
2153:
2148:
2143:
2138:
2133:
2128:
2123:
2118:
2113:
2108:
2103:
2098:
2093:
2088:
2083:
2077:
2075:
2066:
2060:
2059:
2056:
2055:
2053:
2052:
2047:
2042:
2037:
2032:
2027:
2022:
2017:
2012:
2007:
2002:
1997:
1992:
1987:
1982:
1977:
1972:
1967:
1961:
1959:
1956:with infinite
1953:
1952:
1950:
1949:
1944:
1939:
1934:
1929:
1924:
1919:
1918:
1917:
1910:Hypergeometric
1907:
1902:
1897:
1892:
1887:
1881:
1879:
1870:
1864:
1863:
1851:
1850:
1843:
1836:
1828:
1821:
1820:
1805:
1784:
1782:
1779:
1777:
1776:
1762:
1735:Pan, Jianxin;
1732:
1714:(3): 745â752.
1703:
1697:
1684:
1683:
1682:
1676:
1656:
1635:
1621:
1601:
1587:
1574:
1564:(1): 185â201.
1553:
1541:(3): 368â385.
1526:
1520:
1503:
1501:
1498:
1495:
1494:
1483:
1481:, p. 221)
1471:
1464:
1446:
1434:
1422:
1410:
1398:
1386:
1374:
1362:
1348:
1340:Anderson (2004
1332:
1323:
1310:
1292:
1285:
1264:
1211:
1190:
1177:
1175:, p. 27).
1153:
1141:
1139:, p. 368)
1128:
1127:
1125:
1122:
1104:
1101:
1088:
1085:
1071:(particularly
1044:
1024:
1021:
1009:
1006:
973:
970:
950:
947:
897:
894:
873:, such as the
855:
835:
832:
829:
826:
823:
820:
800:
780:
777:
772:
768:
764:
761:
757:
736:
714:
710:
706:
703:
699:
695:
692:
689:
686:
683:
644:
641:
638:
635:
623:
616:
609:
606:
605:
604:
598:
593:
588:
583:
574:
564:
561:
540:
520:
493:
473:
449:
438:
437:
426:
423:
420:
417:
414:
411:
406:
403:
399:
394:
391:
387:
384:
381:
378:
375:
372:
369:
366:
363:
360:
357:
354:
351:
339:has the form:
290:
270:
247:
233:
232:
221:
218:
215:
211:
208:
204:
201:
198:
195:
192:
189:
184:
181:
178:
174:
150:
126:
98:
82:
79:
15:
9:
6:
4:
3:
2:
5575:
5564:
5561:
5559:
5556:
5554:
5551:
5549:
5546:
5545:
5543:
5528:
5527:
5518:
5516:
5515:
5506:
5504:
5503:
5498:
5492:
5490:
5489:
5480:
5479:
5476:
5462:
5459:
5457:
5456:Geostatistics
5454:
5452:
5449:
5447:
5444:
5442:
5439:
5438:
5436:
5434:
5430:
5424:
5423:Psychometrics
5421:
5419:
5416:
5414:
5411:
5409:
5406:
5404:
5401:
5399:
5396:
5394:
5391:
5389:
5386:
5384:
5381:
5379:
5376:
5375:
5373:
5371:
5367:
5361:
5358:
5356:
5353:
5351:
5347:
5344:
5342:
5339:
5337:
5334:
5332:
5329:
5328:
5326:
5324:
5320:
5314:
5311:
5309:
5306:
5304:
5300:
5297:
5295:
5292:
5291:
5289:
5287:
5286:Biostatistics
5283:
5279:
5275:
5270:
5266:
5248:
5247:Log-rank test
5245:
5244:
5242:
5238:
5232:
5229:
5228:
5226:
5224:
5220:
5214:
5211:
5209:
5206:
5204:
5201:
5199:
5196:
5195:
5193:
5191:
5187:
5184:
5182:
5178:
5168:
5165:
5163:
5160:
5158:
5155:
5153:
5150:
5148:
5145:
5144:
5142:
5140:
5136:
5130:
5127:
5125:
5122:
5120:
5118:(BoxâJenkins)
5114:
5112:
5109:
5107:
5104:
5100:
5097:
5096:
5095:
5092:
5091:
5089:
5087:
5083:
5077:
5074:
5072:
5071:DurbinâWatson
5069:
5067:
5061:
5059:
5056:
5054:
5053:DickeyâFuller
5051:
5050:
5048:
5044:
5038:
5035:
5033:
5030:
5028:
5027:Cointegration
5025:
5023:
5020:
5018:
5015:
5013:
5010:
5008:
5005:
5003:
5002:Decomposition
5000:
4999:
4997:
4993:
4990:
4988:
4984:
4974:
4971:
4970:
4969:
4966:
4965:
4964:
4961:
4957:
4954:
4953:
4952:
4949:
4947:
4944:
4942:
4939:
4937:
4934:
4932:
4929:
4927:
4924:
4922:
4919:
4917:
4914:
4913:
4911:
4909:
4905:
4899:
4896:
4894:
4891:
4889:
4886:
4884:
4881:
4879:
4876:
4874:
4873:Cohen's kappa
4871:
4870:
4868:
4866:
4862:
4858:
4854:
4850:
4846:
4842:
4837:
4833:
4819:
4816:
4814:
4811:
4809:
4806:
4804:
4801:
4800:
4798:
4796:
4792:
4786:
4782:
4778:
4772:
4770:
4767:
4766:
4764:
4762:
4758:
4752:
4749:
4747:
4744:
4742:
4739:
4737:
4734:
4732:
4729:
4727:
4726:Nonparametric
4724:
4722:
4719:
4718:
4716:
4712:
4706:
4703:
4701:
4698:
4696:
4693:
4691:
4688:
4687:
4685:
4683:
4679:
4673:
4670:
4668:
4665:
4663:
4660:
4658:
4655:
4653:
4650:
4649:
4647:
4645:
4641:
4635:
4632:
4630:
4627:
4625:
4622:
4620:
4617:
4616:
4614:
4612:
4608:
4604:
4597:
4594:
4592:
4589:
4588:
4584:
4580:
4564:
4561:
4560:
4559:
4556:
4554:
4551:
4549:
4546:
4542:
4539:
4537:
4534:
4533:
4532:
4529:
4528:
4526:
4524:
4520:
4510:
4507:
4503:
4497:
4495:
4489:
4487:
4481:
4480:
4479:
4476:
4475:Nonparametric
4473:
4471:
4465:
4461:
4458:
4457:
4456:
4450:
4446:
4445:Sample median
4443:
4442:
4441:
4438:
4437:
4435:
4433:
4429:
4421:
4418:
4416:
4413:
4411:
4408:
4407:
4406:
4403:
4401:
4398:
4396:
4390:
4388:
4385:
4383:
4380:
4378:
4375:
4373:
4370:
4368:
4366:
4362:
4360:
4357:
4356:
4354:
4352:
4348:
4342:
4340:
4336:
4334:
4332:
4327:
4325:
4320:
4316:
4315:
4312:
4309:
4307:
4303:
4293:
4290:
4288:
4285:
4283:
4280:
4279:
4277:
4275:
4271:
4265:
4262:
4258:
4255:
4254:
4253:
4250:
4246:
4243:
4242:
4241:
4238:
4236:
4233:
4232:
4230:
4228:
4224:
4216:
4213:
4211:
4208:
4207:
4206:
4203:
4201:
4198:
4196:
4193:
4191:
4188:
4186:
4183:
4181:
4178:
4177:
4175:
4173:
4169:
4163:
4160:
4156:
4153:
4149:
4146:
4144:
4141:
4140:
4139:
4136:
4135:
4134:
4131:
4127:
4124:
4122:
4119:
4117:
4114:
4112:
4109:
4108:
4107:
4104:
4103:
4101:
4099:
4095:
4092:
4090:
4086:
4080:
4077:
4075:
4072:
4068:
4065:
4064:
4063:
4060:
4058:
4055:
4051:
4050:loss function
4048:
4047:
4046:
4043:
4039:
4036:
4034:
4031:
4029:
4026:
4025:
4024:
4021:
4019:
4016:
4014:
4011:
4007:
4004:
4002:
3999:
3997:
3991:
3988:
3987:
3986:
3983:
3979:
3976:
3974:
3971:
3969:
3966:
3965:
3964:
3961:
3957:
3954:
3952:
3949:
3948:
3947:
3944:
3940:
3937:
3936:
3935:
3932:
3928:
3925:
3924:
3923:
3920:
3918:
3915:
3913:
3910:
3908:
3905:
3904:
3902:
3900:
3896:
3892:
3888:
3883:
3879:
3865:
3862:
3860:
3857:
3855:
3852:
3850:
3847:
3846:
3844:
3842:
3838:
3832:
3829:
3827:
3824:
3822:
3819:
3818:
3816:
3812:
3806:
3803:
3801:
3798:
3796:
3793:
3791:
3788:
3786:
3783:
3781:
3778:
3776:
3773:
3772:
3770:
3768:
3764:
3758:
3755:
3753:
3752:Questionnaire
3750:
3748:
3745:
3741:
3738:
3736:
3733:
3732:
3731:
3728:
3727:
3725:
3723:
3719:
3713:
3710:
3708:
3705:
3703:
3700:
3698:
3695:
3693:
3690:
3688:
3685:
3683:
3680:
3678:
3675:
3674:
3672:
3670:
3666:
3662:
3658:
3653:
3649:
3635:
3632:
3630:
3627:
3625:
3622:
3620:
3617:
3615:
3612:
3610:
3607:
3605:
3602:
3600:
3597:
3595:
3592:
3590:
3587:
3585:
3582:
3580:
3579:Control chart
3577:
3575:
3572:
3570:
3567:
3565:
3562:
3561:
3559:
3557:
3553:
3547:
3544:
3540:
3537:
3535:
3532:
3531:
3530:
3527:
3525:
3522:
3520:
3517:
3516:
3514:
3512:
3508:
3502:
3499:
3497:
3494:
3492:
3489:
3488:
3486:
3482:
3476:
3473:
3472:
3470:
3468:
3464:
3452:
3449:
3447:
3444:
3442:
3439:
3438:
3437:
3434:
3432:
3429:
3428:
3426:
3424:
3420:
3414:
3411:
3409:
3406:
3404:
3401:
3399:
3396:
3394:
3391:
3389:
3386:
3384:
3381:
3380:
3378:
3376:
3372:
3366:
3363:
3361:
3358:
3354:
3351:
3349:
3346:
3344:
3341:
3339:
3336:
3334:
3331:
3329:
3326:
3324:
3321:
3319:
3316:
3314:
3311:
3309:
3306:
3305:
3304:
3301:
3300:
3298:
3296:
3292:
3289:
3287:
3283:
3279:
3275:
3270:
3266:
3260:
3257:
3255:
3252:
3251:
3248:
3244:
3237:
3232:
3230:
3225:
3223:
3218:
3217:
3214:
3202:
3194:
3192:
3184:
3183:
3180:
3174:
3171:
3169:
3166:
3164:
3161:
3159:
3156:
3154:
3151:
3149:
3146:
3144:
3141:
3139:
3136:
3134:
3131:
3129:
3126:
3124:
3121:
3120:
3118:
3114:
3108:
3105:
3102:
3098:
3096:
3093:
3090:
3086:
3085:
3083:
3081:
3076:
3072:
3066:
3063:
3061:
3058:
3055:
3051:
3049:
3046:
3043:
3039:
3037:
3034:
3031:
3027:
3025:
3022:
3020:
3017:
3015:
3012:
3010:
3007:
3005:
3002:
3000:
2997:
2995:
2992:
2989:
2988:
2982:
2981:
2979:
2977:
2973:
2965:
2962:
2960:
2957:
2955:
2952:
2950:
2947:
2946:
2945:
2942:
2938:
2935:
2934:
2933:
2930:
2928:
2927:
2922:
2920:
2919:Matrix normal
2917:
2915:
2912:
2909:
2908:
2903:
2899:
2896:
2895:
2894:
2891:
2889:
2888:
2885:Multivariate
2883:
2881:
2878:
2876:
2873:
2871:
2868:
2864:
2861:
2860:
2859:
2856:
2853:
2849:
2845:
2842:
2840:
2837:
2836:
2835:
2832:
2830:
2827:
2824:
2820:
2819:
2817:
2815:
2812:Multivariate
2809:
2799:
2796:
2795:
2793:
2787:
2784:
2778:
2768:
2765:
2763:
2760:
2758:
2756:
2752:
2750:
2748:
2744:
2742:
2740:
2736:
2734:
2732:
2727:
2725:
2723:
2718:
2716:
2714:
2709:
2707:
2705:
2700:
2698:
2696:
2691:
2689:
2686:
2684:
2681:
2679:
2676:
2674:
2671:
2670:
2668:
2664:with support
2662:
2656:
2653:
2651:
2648:
2646:
2643:
2641:
2640:
2635:
2633:
2630:
2628:
2625:
2623:
2620:
2618:
2615:
2613:
2610:
2608:
2607:
2602:
2600:
2597:
2593:
2590:
2589:
2588:
2585:
2583:
2580:
2578:
2577:
2569:
2567:
2564:
2562:
2559:
2557:
2554:
2552:
2549:
2547:
2544:
2542:
2539:
2537:
2536:
2531:
2529:
2526:
2524:
2523:
2518:
2516:
2513:
2511:
2508:
2507:
2505:
2501:on the whole
2497:
2491:
2488:
2484:
2481:
2480:
2479:
2476:
2474:
2473:type-2 Gumbel
2471:
2469:
2466:
2464:
2461:
2459:
2456:
2454:
2451:
2449:
2446:
2444:
2441:
2439:
2436:
2434:
2431:
2429:
2426:
2424:
2421:
2419:
2416:
2414:
2411:
2409:
2406:
2404:
2401:
2399:
2396:
2394:
2391:
2389:
2386:
2384:
2381:
2379:
2376:
2374:
2371:
2367:
2364:
2363:
2362:
2359:
2357:
2355:
2350:
2348:
2345:
2343:
2342:Half-logistic
2340:
2336:
2333:
2332:
2331:
2328:
2326:
2323:
2319:
2316:
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2298:Folded normal
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2013:
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1162:
1161:Johnson (1987
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1100:
1098:
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1077:vectorization
1074:
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1066:
1062:
1061:linear models
1058:
1042:
1022:
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1005:
1003:
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989:
985:
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980:multivariate
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581:-distribution
580:
577:Multivariate
575:
573:
570:
569:
568:
560:
558:
554:
518:
511:
510:median vector
507:
506:random vector
504:-dimensional
491:
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328:for example.
327:
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319:pseudo-random
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5493:
5486:
5398:Econometrics
5348: /
5331:Chemometrics
5308:Epidemiology
5301: /
5274:Applications
5116:ARIMA model
5063:Q-statistic
5012:Stationarity
4967:
4908:Multivariate
4851: /
4847: /
4845:Multivariate
4843: /
4783: /
4779: /
4553:Bayes factor
4452:Signed rank
4364:
4338:
4330:
4318:
4013:Completeness
3849:Cohort study
3747:Opinion poll
3682:Missing data
3669:Study design
3624:Scatter plot
3546:Scatter plot
3539:Spearman's Ï
3501:Grouped data
3132:
3100:
3088:
3054:Multivariate
3053:
3041:
3029:
3024:Wrapped LĂ©vy
2984:
2932:Matrix gamma
2925:
2905:
2893:Normal-gamma
2886:
2852:Continuous:
2851:
2822:
2767:Tukey lambda
2754:
2746:
2741:-exponential
2738:
2730:
2721:
2712:
2703:
2697:-exponential
2694:
2638:
2605:
2572:
2534:
2521:
2448:Poly-Weibull
2393:Log-logistic
2353:
2352:Hotelling's
2284:
2126:Logit-normal
2000:GaussâKuzmin
1995:FloryâSchulz
1876:with finite
1796:
1741:
1737:Fang, Kaitai
1711:
1707:
1688:
1667:
1639:
1612:
1609:Kotz, Samuel
1578:
1561:
1557:
1538:
1534:
1511:
1486:
1474:
1455:
1449:
1437:
1425:
1413:
1401:
1389:
1377:
1365:
1343:
1335:
1326:
1313:
1276:
1224:
1220:
1214:
1203:. Retrieved
1193:
1185:
1180:
1166:
1156:
1144:
1132:
1106:
1090:
1065:growth curve
1056:
1011:
999:
994:
987:
984:distribution
981:
977:
975:
959:
952:
949:Applications
942:
938:
930:
926:
922:
920:
912:uncorrelated
909:
878:
868:
669:
660:
620:
613:
611:
578:
566:
439:
336:
330:
302:
234:
114:
84:
62:
55:
49:
28:
18:
5526:WikiProject
5441:Cartography
5403:Jurimetrics
5355:Reliability
5086:Time domain
5065:(LjungâBox)
4987:Time-series
4865:Categorical
4849:Time-series
4841:Categorical
4776:(Bernoulli)
4611:Correlation
4591:Correlation
4387:JarqueâBera
4359:Chi-squared
4121:M-estimator
4074:Asymptotics
4018:Sufficiency
3785:Interaction
3697:Replication
3677:Effect size
3634:Violin plot
3614:Radar chart
3594:Forest plot
3584:Correlogram
3534:Kendall's Ï
3138:Exponential
2987:directional
2976:Directional
2863:Generalized
2834:Multinomial
2789:continuous-
2729:Kaniadakis
2720:Kaniadakis
2711:Kaniadakis
2702:Kaniadakis
2693:Kaniadakis
2645:TracyâWidom
2622:Skew normal
2604:Noncentral
2388:Log-Laplace
2366:Generalized
2347:Half-normal
2313:Generalized
2277:Logarithmic
2262:Exponential
2216:Chi-squared
2156:U-quadratic
2121:Kumaraswamy
2063:Continuous
2010:Logarithmic
1905:Categorical
1664:Originally
995:generalized
326:simulations
323:Monte Carlo
69:, like the
63:generalized
21:probability
5542:Categories
5393:Demography
5111:ARMA model
4916:Regression
4493:(Friedman)
4454:(Wilcoxon)
4392:Normality
4382:Lilliefors
4329:Student's
4205:Resampling
4079:Robustness
4067:divergence
4057:Efficiency
3995:(monotone)
3990:Likelihood
3907:Population
3740:Stratified
3692:Population
3511:Dependence
3467:Count data
3398:Percentile
3375:Dispersion
3308:Arithmetic
3243:Statistics
3133:Elliptical
3089:Degenerate
3075:Degenerate
2823:Discrete:
2782:univariate
2637:Student's
2592:Asymmetric
2571:Johnson's
2499:supported
2443:Phase-type
2398:Log-normal
2383:Log-Cauchy
2373:Kolmogorov
2291:Noncentral
2221:Noncentral
2201:Beta prime
2151:Triangular
2146:Reciprocal
2116:IrwinâHall
2065:univariate
2045:YuleâSimon
1927:Rademacher
1869:univariate
1806:0898640482
1677:0792326083
1588:3540176519
1500:References
1465:0123982308
1205:2017-05-26
962:portfolios
933:with full
665:ellipsoids
608:Properties
235:for some
81:Definition
52:statistics
25:statistics
4774:Logistic
4541:posterior
4467:Rank sum
4215:Jackknife
4210:Bootstrap
4028:Bootstrap
3963:Parameter
3912:Statistic
3707:Statistic
3619:Run chart
3604:Pie chart
3599:Histogram
3589:Fan chart
3564:Bar chart
3446:L-moments
3333:Geometric
2858:Dirichlet
2839:Dirichlet
2749:-Gaussian
2724:-Logistic
2561:Holtsmark
2533:Gaussian
2520:Fisher's
2503:real line
2005:Geometric
1985:Delaporte
1890:Bernoulli
1867:Discrete
1631:123206055
1597:622932253
1234:1302.6498
1020:α
988:classical
893:μ
883:symmetric
760:−
702:−
539:Σ
519:μ
419:μ
416:−
402:−
398:Σ
386:μ
383:−
368:⋅
289:ψ
269:Σ
246:μ
214:Σ
200:ψ
183:μ
180:−
173:ϕ
125:ϕ
56:classical
45:ellipsoid
5488:Category
5181:Survival
5058:Johansen
4781:Binomial
4736:Isotonic
4323:(normal)
3968:location
3775:Blocking
3730:Sampling
3609:QâQ plot
3574:Box plot
3556:Graphics
3451:Skewness
3441:Kurtosis
3413:Variance
3343:Heronian
3338:Harmonic
3191:Category
3123:Circular
3116:Families
3101:Singular
3080:singular
2844:Negative
2791:discrete
2757:-Weibull
2715:-Weibull
2599:Logistic
2483:Discrete
2453:Rayleigh
2433:Nakagami
2356:-squared
2330:Gompertz
2179:interval
1915:Negative
1900:Binomial
1815:20490516
1772:44162563
1739:(2007).
1510:(2004).
1116:and the
935:row rank
846:for all
655:) is an
563:Examples
393:′
210:′
5514:Commons
5461:Kriging
5346:Process
5303:studies
5162:Wavelet
4995:General
4162:Plug-in
3956:L space
3735:Cluster
3436:Moments
3254:Outline
3201:Commons
3173:Wrapped
3168:Tweedie
3163:Pearson
3158:Mixture
3065:Bingham
2964:Complex
2954:Inverse
2944:Wishart
2937:Inverse
2924:Matrix
2898:Inverse
2814:(joint)
2733:-Erlang
2587:Laplace
2478:Weibull
2335:Shifted
2318:Inverse
2303:Fréchet
2226:Inverse
2161:Uniform
2081:Arcsine
2040:Skellam
2035:Poisson
1958:support
1932:Soliton
1885:Benford
1878:support
1728:2328079
1259:3909632
1239:Bibcode
657:ellipse
460:is the
258:, some
113:has an
43:and an
41:ellipse
5383:Census
4973:Normal
4921:Manova
4741:Robust
4491:2-way
4483:1-way
4321:-test
3992:
3569:Biplot
3360:Median
3353:Lehmer
3295:Center
3107:Cantor
2949:Normal
2780:Mixed
2706:-Gamma
2632:Stable
2582:Landau
2556:Gumbel
2510:Cauchy
2438:Pareto
2250:Erlang
2231:Scaled
2186:Benini
2025:Panjer
1813:
1803:
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1035:where
982:normal
885:about
484:is an
440:where
5007:Trend
4536:prior
4478:anova
4367:-test
4341:-test
4333:-test
4240:Power
4185:Pivot
3978:shape
3973:scale
3423:Shape
3403:Range
3348:Heinz
3323:Cubic
3259:Index
2829:Ewens
2655:Voigt
2627:Slash
2408:Lomax
2403:Log-t
2308:Gamma
2255:Hyper
2245:Davis
2240:Dagum
2096:Bates
2086:ARGUS
1970:Borel
1746:(PDF)
1724:JSTOR
1255:S2CID
1229:arXiv
1124:Notes
551:is a
508:with
307:field
109:on a
67:heavy
27:, an
5240:Test
4440:Sign
4292:Wald
3365:Mode
3303:Mean
3078:and
3036:Kent
2463:Rice
2378:LĂ©vy
2206:Burr
2136:PERT
2101:Beta
2050:Zeta
1942:Zipf
1859:list
1811:OCLC
1801:ISBN
1768:OCLC
1758:ISBN
1693:ISBN
1672:ISBN
1652:ISBN
1627:OCLC
1617:ISBN
1593:OCLC
1583:ISBN
1516:ISBN
1460:ISBN
1281:ISBN
1075:and
871:mean
776:>
670:The
303:real
23:and
4420:BIC
4415:AIC
2914:LKJ
2211:Chi
1750:doi
1716:doi
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