3763:
3749:
3787:
3775:
434:
667:
199:
440:
1154:
168:
429:{\displaystyle S={\frac {{\hat {\mu }}_{3}}{{\hat {\sigma }}^{3}}}={\frac {{\frac {1}{n}}\sum _{i=1}^{n}(x_{i}-{\bar {x}})^{3}}{\left({\frac {1}{n}}\sum _{i=1}^{n}(x_{i}-{\bar {x}})^{2}\right)^{3/2}}},}
662:{\displaystyle K={\frac {{\hat {\mu }}_{4}}{{\hat {\sigma }}^{4}}}={\frac {{\frac {1}{n}}\sum _{i=1}^{n}(x_{i}-{\bar {x}})^{4}}{\left({\frac {1}{n}}\sum _{i=1}^{n}(x_{i}-{\bar {x}})^{2}\right)^{2}}},}
1026:'s implementation, the chi-squared approximation for the JB statistic's distribution is only used for large sample sizes (> 2000). For smaller samples, it uses a table derived from
815:
856:
being zero. Samples from a normal distribution have an expected skewness of 0 and an expected excess kurtosis of 0 (which is the same as a kurtosis of 3). As the definition of
742:
706:
775:
1056:
78:
863:
For small samples the chi-squared approximation is overly sensitive, often rejecting the null hypothesis when it is true. Furthermore, the distribution of
1407:; Bera, Anil K. (1981). "Efficient tests for normality, homoscedasticity and serial independence of regression residuals: Monte Carlo evidence".
2884:
3389:
1050:
According to Robert Hall, David Lilien, et al. (1995) when using this test along with multiple regression analysis the right estimate is:
1042:
The statistic was derived by Carlos M. Jarque and Anil K. Bera while working on their Ph.D. Thesis at the
Australian National University.
3539:
3163:
1804:
2937:
3376:
1799:
1499:
1383:; Bera, Anil K. (1980). "Efficient tests for normality, homoscedasticity and serial independence of regression residuals".
62:. The test statistic is always nonnegative. If it is far from zero, it signals the data do not have a normal distribution.
2403:
1551:
3186:
3078:
1249:
1239:
includes a built in function called, JarqueBeraALMTest and is not limited to testing against a
Gaussian distribution.
871:
3791:
3364:
3238:
17:
3422:
3083:
2828:
2199:
1789:
837:
3473:
2685:
2492:
2381:
2339:
893:-values approximated by a chi-squared distribution that differ from their true alpha levels for small samples.
841:
2413:
3716:
2675:
1578:
1208:
3267:
3216:
3201:
3191:
3060:
2932:
2899:
2725:
2680:
2510:
1188:
1270:
784:
3779:
3611:
3412:
3336:
2637:
2391:
2060:
1524:
1176:
3496:
3468:
3463:
3211:
2970:
2876:
2856:
2764:
2475:
2293:
1776:
1648:
711:
675:
3228:
2996:
2717:
2642:
2571:
2500:
2420:
2408:
2278:
2266:
2259:
1967:
1688:
3813:
3711:
3478:
3341:
3026:
2991:
2955:
2740:
2182:
2091:
2050:
1962:
1653:
1492:
1352:
1214:
833:
3620:
3233:
3173:
3110:
2748:
2732:
2470:
2332:
2322:
2172:
2086:
1211:
statsmodels includes an implementation of the Jarque–Bera test, "statsmodels.stats.stattools.py".
1027:
1292:
751:
3658:
3588:
3381:
3318:
3073:
2960:
1957:
1854:
1761:
1640:
1539:
1012:
3683:
3625:
3568:
3394:
3287:
3196:
2922:
2806:
2665:
2657:
2547:
2539:
2354:
2250:
2228:
2187:
2152:
2119:
2065:
2040:
1995:
1934:
1894:
1696:
1519:
1334:
1316:
878:
3606:
3181:
3130:
3106:
3068:
2986:
2965:
2917:
2796:
2774:
2743:
2529:
2480:
2398:
2371:
2327:
2283:
2045:
1821:
1701:
8:
3753:
3678:
3601:
3282:
3046:
3039:
3001:
2909:
2889:
2861:
2594:
2460:
2455:
2445:
2437:
2255:
2216:
2106:
2096:
2005:
1784:
1740:
1658:
1583:
1485:
1431:; Bera, Anil K. (1987). "A test for normality of observations and regression residuals".
1236:
1179:
includes an implementation of the Jarque–Bera test in C++, C#, Delphi, Visual Basic, etc.
1149:{\displaystyle {\mathit {JB}}={\frac {n-k}{6}}\left(S^{2}+{\frac {1}{4}}(K-3)^{2}\right)}
845:
829:
51:
3767:
3578:
3432:
3328:
3277:
3153:
3050:
3034:
3011:
2788:
2522:
2505:
2465:
2376:
2271:
2233:
2204:
2164:
2124:
2070:
1987:
1673:
1668:
1448:
163:{\displaystyle {\mathit {JB}}={\frac {n}{6}}\left(S^{2}+{\frac {1}{4}}(K-3)^{2}\right)}
3762:
3673:
3643:
3635:
3455:
3446:
3371:
3302:
3158:
3143:
3118:
3006:
2947:
2813:
2801:
2427:
2344:
2288:
2211:
2055:
1977:
1756:
1630:
1420:
1396:
3698:
3653:
3417:
3404:
3297:
3272:
3206:
3138:
3016:
2624:
2517:
2450:
2363:
2310:
2129:
2000:
1794:
1678:
1593:
1560:
1440:
1416:
1392:
3615:
3359:
3221:
3148:
2823:
2697:
2670:
2647:
2616:
2243:
2238:
2192:
1922:
1573:
853:
849:
39:
3105:
3564:
3559:
2022:
1952:
1598:
745:
66:
3807:
3721:
3688:
3551:
3512:
3323:
3292:
2756:
2710:
2315:
2017:
1844:
1608:
1603:
1428:
1404:
1380:
55:
3663:
3596:
3573:
3488:
2818:
2114:
2012:
1947:
1889:
1874:
1811:
1766:
886:
875:
59:
1205:
includes an implementation of the Jarque–Bera test, the function "jbtest".
3706:
3668:
3351:
3252:
3114:
2927:
2894:
2386:
2303:
2298:
1942:
1899:
1879:
1859:
1849:
1618:
2552:
2032:
1732:
1663:
1613:
1588:
1508:
1452:
31:
2705:
2557:
2177:
1972:
1884:
1869:
1864:
1829:
1167:
is the number of regressors when examining residuals to an equation.
1444:
2221:
1839:
1716:
1711:
1706:
1335:"moments: Moments, cumulants, skewness, kurtosis and related tests"
818:
190:
182:
47:
43:
177:
is the number of observations (or degrees of freedom in general);
3726:
3427:
864:
3648:
2629:
2603:
2583:
1834:
1625:
1202:
1023:
1016:
903:-values equivalents to true alpha levels at given sample sizes
1477:
1182:
1568:
860:
shows, any deviation from this increases the JB statistic.
778:
1045:
1317:"tseries: Time Series Analysis and Computational Finance"
1065:
852:
is a joint hypothesis of the skewness being zero and the
87:
1462:
Introduction and the theory and practice of econometrics
1469:
Hall, Robert E.; Lilien, David M.; et al. (1995).
1059:
787:
754:
714:
678:
443:
202:
81:
3390:
Autoregressive conditional heteroskedasticity (ARCH)
1191:includes an implementation of the Jarque-Bera test
2852:
1353:"JarqueBeraALMTest—Wolfram Language Documentation"
1217:includes implementations of the Jarque–Bera test:
1185:includes an implementation of the Jarque–Bera test
1148:
824:If the data comes from a normal distribution, the
817:is the estimate of the second central moment, the
809:
769:
736:
700:
661:
428:
162:
3805:
2938:Multivariate adaptive regression splines (MARS)
1252:, another test based on kurtosis and skewness.
1493:
1011:(These values have been approximated using
1538:
1500:
1486:
1468:
1427:
1403:
1379:
2151:
1263:
844:the hypothesis that the data are from a
1046:Jarque–Bera test in regression analysis
14:
3806:
3464:Kaplan–Meier estimator (product limit)
744:are the estimates of third and fourth
3537:
3104:
2851:
2150:
1920:
1537:
1481:
1459:
42:test of whether sample data have the
3774:
3474:Accelerated failure time (AFT) model
810:{\displaystyle {\hat {\sigma }}^{2}}
3786:
3069:Analysis of variance (ANOVA, anova)
1921:
1271:"Analysis of the JB-Test in MATLAB"
24:
3164:Cochran–Mantel–Haenszel statistics
1790:Pearson product-moment correlation
1373:
1170:
1163:is the number of observations and
1062:
840:, so the statistic can be used to
84:
25:
3825:
1464:(3rd ed.). pp. 890–892.
889:rate. The table below shows some
737:{\displaystyle {\hat {\mu }}_{4}}
701:{\displaystyle {\hat {\mu }}_{3}}
3785:
3773:
3761:
3748:
3747:
3538:
1433:International Statistical Review
3423:Least-squares spectral analysis
885:-values. This leads to a large
2404:Mean-unbiased minimum-variance
1507:
1345:
1327:
1309:
1285:
1132:
1119:
795:
761:
722:
686:
634:
627:
605:
558:
551:
529:
478:
459:
393:
386:
364:
317:
310:
288:
237:
218:
146:
133:
13:
1:
3717:Geographic information system
2933:Simultaneous equations models
1256:
2900:Coefficient of determination
2511:Uniformly most powerful test
1421:10.1016/0165-1765(81)90035-5
1397:10.1016/0165-1765(80)90024-5
7:
3469:Proportional hazards models
3413:Spectral density estimation
3395:Vector autoregression (VAR)
2829:Maximum posterior estimator
2061:Randomized controlled trial
1460:Judge; et al. (1988).
1250:D'Agostino's K-squared test
1243:
10:
3830:
3229:Multivariate distributions
1649:Average absolute deviation
1037:
770:{\displaystyle {\bar {x}}}
54:. The test is named after
3743:
3697:
3634:
3587:
3550:
3546:
3533:
3505:
3487:
3454:
3445:
3403:
3350:
3311:
3260:
3251:
3217:Structural equation model
3172:
3129:
3125:
3100:
3059:
3025:
2979:
2946:
2908:
2875:
2871:
2847:
2787:
2696:
2615:
2579:
2570:
2553:Score/Lagrange multiplier
2538:
2491:
2436:
2362:
2353:
2163:
2159:
2146:
2105:
2079:
2031:
1986:
1968:Sample size determination
1933:
1929:
1916:
1820:
1775:
1749:
1731:
1687:
1639:
1559:
1550:
1546:
1533:
1515:
3712:Environmental statistics
3234:Elliptical distributions
3027:Generalized linear model
2956:Simple linear regression
2726:Hodges–Lehmann estimator
2183:Probability distribution
2092:Stochastic approximation
1654:Coefficient of variation
1030:in order to interpolate
834:chi-squared distribution
3372:Cross-correlation (XCF)
2980:Non-standard predictors
2414:Lehmann–Scheffé theorem
2087:Adaptive clinical trial
1028:Monte Carlo simulations
881:, especially for small
3768:Mathematics portal
3589:Engineering statistics
3497:Nelson–Aalen estimator
3074:Analysis of covariance
2961:Ordinary least squares
2885:Pearson product-moment
2289:Statistical functional
2200:Empirical distribution
2033:Controlled experiments
1762:Frequency distribution
1540:Descriptive statistics
1150:
1013:Monte Carlo simulation
811:
771:
738:
702:
663:
604:
528:
430:
363:
287:
164:
3684:Population statistics
3626:System identification
3360:Autocorrelation (ACF)
3288:Exponential smoothing
3202:Discriminant analysis
3197:Canonical correlation
3061:Partition of variance
2923:Regression validation
2767:(Jonckheere–Terpstra)
2666:Likelihood-ratio test
2355:Frequentist inference
2267:Location–scale family
2188:Sampling distribution
2153:Statistical inference
2120:Cross-sectional study
2107:Observational studies
2066:Randomized experiment
1895:Stem-and-leaf display
1697:Central limit theorem
1357:reference.wolfram.com
1151:
879:unimodal distribution
812:
772:
739:
703:
664:
584:
508:
431:
343:
267:
165:
3607:Probabilistic design
3192:Principal components
3035:Exponential families
2987:Nonlinear regression
2966:General linear model
2928:Mixed effects models
2918:Errors and residuals
2895:Confounding variable
2797:Bayesian probability
2775:Van der Waerden test
2765:Ordered alternative
2530:Multiple comparisons
2409:Rao–Blackwellization
2372:Estimating equations
2328:Statistical distance
2046:Factorial experiment
1579:Arithmetic-Geometric
1057:
872:uniform distribution
785:
752:
712:
676:
441:
200:
79:
3679:Official statistics
3602:Methods engineering
3283:Seasonal adjustment
3051:Poisson regressions
2971:Bayesian regression
2910:Regression analysis
2890:Partial correlation
2862:Regression analysis
2461:Prediction interval
2456:Likelihood interval
2446:Confidence interval
2438:Interval estimation
2399:Unbiased estimators
2217:Model specification
2097:Up-and-down designs
1785:Partial correlation
1741:Index of dispersion
1659:Interquartile range
1293:"Time series tests"
1225:, for example, and
904:
846:normal distribution
52:normal distribution
3699:Spatial statistics
3579:Medical statistics
3479:First hitting time
3433:Whittle likelihood
3084:Degrees of freedom
3079:Multivariate ANOVA
3012:Heteroscedasticity
2824:Bayesian estimator
2789:Bayesian inference
2638:Kolmogorov–Smirnov
2523:Randomization test
2493:Testing hypotheses
2466:Tolerance interval
2377:Maximum likelihood
2272:Exponential family
2205:Density estimation
2165:Statistical theory
2125:Natural experiment
2071:Scientific control
1988:Survey methodology
1674:Standard deviation
1146:
898:
838:degrees of freedom
807:
767:
734:
698:
659:
426:
160:
3801:
3800:
3739:
3738:
3735:
3734:
3674:National accounts
3644:Actuarial science
3636:Social statistics
3529:
3528:
3525:
3524:
3521:
3520:
3456:Survival function
3441:
3440:
3303:Granger causality
3144:Contingency table
3119:Survival analysis
3096:
3095:
3092:
3091:
2948:Linear regression
2843:
2842:
2839:
2838:
2814:Credible interval
2783:
2782:
2566:
2565:
2382:Method of moments
2251:Parametric family
2212:Statistical model
2142:
2141:
2138:
2137:
2056:Random assignment
1978:Statistical power
1912:
1911:
1908:
1907:
1757:Contingency table
1727:
1726:
1594:Generalized/power
1471:EViews User Guide
1429:Jarque, Carlos M.
1409:Economics Letters
1405:Jarque, Carlos M.
1385:Economics Letters
1381:Jarque, Carlos M.
1117:
1089:
1007:
1006:
798:
764:
725:
689:
654:
630:
582:
554:
506:
490:
481:
462:
421:
389:
341:
313:
265:
249:
240:
221:
131:
103:
16:(Redirected from
3821:
3789:
3788:
3777:
3776:
3766:
3765:
3751:
3750:
3654:Crime statistics
3548:
3547:
3535:
3534:
3452:
3451:
3418:Fourier analysis
3405:Frequency domain
3385:
3332:
3298:Structural break
3258:
3257:
3207:Cluster analysis
3154:Log-linear model
3127:
3126:
3102:
3101:
3043:
3017:Homoscedasticity
2873:
2872:
2849:
2848:
2768:
2760:
2752:
2751:(Kruskal–Wallis)
2736:
2721:
2676:Cross validation
2661:
2643:Anderson–Darling
2590:
2577:
2576:
2548:Likelihood-ratio
2540:Parametric tests
2518:Permutation test
2501:1- & 2-tails
2392:Minimum distance
2364:Point estimation
2360:
2359:
2311:Optimal decision
2262:
2161:
2160:
2148:
2147:
2130:Quasi-experiment
2080:Adaptive designs
1931:
1930:
1918:
1917:
1795:Rank correlation
1557:
1556:
1548:
1547:
1535:
1534:
1502:
1495:
1488:
1479:
1478:
1474:
1465:
1456:
1424:
1400:
1367:
1366:
1364:
1363:
1349:
1343:
1342:
1331:
1325:
1324:
1313:
1307:
1306:
1304:
1303:
1289:
1283:
1282:
1280:
1278:
1267:
1219:jarque.bera.test
1155:
1153:
1152:
1147:
1145:
1141:
1140:
1139:
1118:
1110:
1105:
1104:
1090:
1085:
1074:
1069:
1068:
905:
897:
816:
814:
813:
808:
806:
805:
800:
799:
791:
776:
774:
773:
768:
766:
765:
757:
748:, respectively,
743:
741:
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733:
732:
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718:
707:
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598:
583:
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541:
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507:
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474:
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469:
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266:
258:
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155:
154:
153:
132:
124:
119:
118:
104:
96:
91:
90:
36:Jarque–Bera test
21:
18:Jarque-Bera test
3829:
3828:
3824:
3823:
3822:
3820:
3819:
3818:
3814:Normality tests
3804:
3803:
3802:
3797:
3760:
3731:
3693:
3630:
3616:quality control
3583:
3565:Clinical trials
3542:
3517:
3501:
3489:Hazard function
3483:
3437:
3399:
3383:
3346:
3342:Breusch–Godfrey
3330:
3307:
3247:
3222:Factor analysis
3168:
3149:Graphical model
3121:
3088:
3055:
3041:
3021:
2975:
2942:
2904:
2867:
2866:
2835:
2779:
2766:
2758:
2750:
2734:
2719:
2698:Rank statistics
2692:
2671:Model selection
2659:
2617:Goodness of fit
2611:
2588:
2562:
2534:
2487:
2432:
2421:Median unbiased
2349:
2260:
2193:Order statistic
2155:
2134:
2101:
2075:
2027:
1982:
1925:
1923:Data collection
1904:
1816:
1771:
1745:
1723:
1683:
1635:
1552:Continuous data
1542:
1529:
1511:
1506:
1445:10.2307/1403192
1376:
1374:Further reading
1371:
1370:
1361:
1359:
1351:
1350:
1346:
1333:
1332:
1328:
1315:
1314:
1310:
1301:
1299:
1291:
1290:
1286:
1276:
1274:
1269:
1268:
1264:
1259:
1246:
1229:in the package
1221:in the package
1197:HypothesisTests
1173:
1171:Implementations
1135:
1131:
1109:
1100:
1096:
1095:
1091:
1075:
1073:
1061:
1060:
1058:
1055:
1054:
1048:
1040:
870:departs from a
854:excess kurtosis
850:null hypothesis
801:
790:
789:
788:
786:
783:
782:
756:
755:
753:
750:
749:
746:central moments
728:
717:
716:
715:
713:
710:
709:
692:
681:
680:
679:
677:
674:
673:
648:
637:
633:
622:
621:
612:
608:
599:
588:
574:
573:
569:
568:
561:
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471:
465:
454:
453:
452:
450:
442:
439:
438:
411:
407:
396:
392:
381:
380:
371:
367:
358:
347:
333:
332:
328:
327:
320:
316:
305:
304:
295:
291:
282:
271:
257:
256:
254:
243:
232:
231:
230:
224:
213:
212:
211:
209:
201:
198:
197:
149:
145:
123:
114:
110:
109:
105:
95:
83:
82:
80:
77:
76:
40:goodness-of-fit
28:
23:
22:
15:
12:
11:
5:
3827:
3817:
3816:
3799:
3798:
3796:
3795:
3783:
3771:
3757:
3744:
3741:
3740:
3737:
3736:
3733:
3732:
3730:
3729:
3724:
3719:
3714:
3709:
3703:
3701:
3695:
3694:
3692:
3691:
3686:
3681:
3676:
3671:
3666:
3661:
3656:
3651:
3646:
3640:
3638:
3632:
3631:
3629:
3628:
3623:
3618:
3609:
3604:
3599:
3593:
3591:
3585:
3584:
3582:
3581:
3576:
3571:
3562:
3560:Bioinformatics
3556:
3554:
3544:
3543:
3531:
3530:
3527:
3526:
3523:
3522:
3519:
3518:
3516:
3515:
3509:
3507:
3503:
3502:
3500:
3499:
3493:
3491:
3485:
3484:
3482:
3481:
3476:
3471:
3466:
3460:
3458:
3449:
3443:
3442:
3439:
3438:
3436:
3435:
3430:
3425:
3420:
3415:
3409:
3407:
3401:
3400:
3398:
3397:
3392:
3387:
3379:
3374:
3369:
3368:
3367:
3365:partial (PACF)
3356:
3354:
3348:
3347:
3345:
3344:
3339:
3334:
3326:
3321:
3315:
3313:
3312:Specific tests
3309:
3308:
3306:
3305:
3300:
3295:
3290:
3285:
3280:
3275:
3270:
3264:
3262:
3255:
3249:
3248:
3246:
3245:
3244:
3243:
3242:
3241:
3226:
3225:
3224:
3214:
3212:Classification
3209:
3204:
3199:
3194:
3189:
3184:
3178:
3176:
3170:
3169:
3167:
3166:
3161:
3159:McNemar's test
3156:
3151:
3146:
3141:
3135:
3133:
3123:
3122:
3098:
3097:
3094:
3093:
3090:
3089:
3087:
3086:
3081:
3076:
3071:
3065:
3063:
3057:
3056:
3054:
3053:
3037:
3031:
3029:
3023:
3022:
3020:
3019:
3014:
3009:
3004:
2999:
2997:Semiparametric
2994:
2989:
2983:
2981:
2977:
2976:
2974:
2973:
2968:
2963:
2958:
2952:
2950:
2944:
2943:
2941:
2940:
2935:
2930:
2925:
2920:
2914:
2912:
2906:
2905:
2903:
2902:
2897:
2892:
2887:
2881:
2879:
2869:
2868:
2865:
2864:
2859:
2853:
2845:
2844:
2841:
2840:
2837:
2836:
2834:
2833:
2832:
2831:
2821:
2816:
2811:
2810:
2809:
2804:
2793:
2791:
2785:
2784:
2781:
2780:
2778:
2777:
2772:
2771:
2770:
2762:
2754:
2738:
2735:(Mann–Whitney)
2730:
2729:
2728:
2715:
2714:
2713:
2702:
2700:
2694:
2693:
2691:
2690:
2689:
2688:
2683:
2678:
2668:
2663:
2660:(Shapiro–Wilk)
2655:
2650:
2645:
2640:
2635:
2627:
2621:
2619:
2613:
2612:
2610:
2609:
2601:
2592:
2580:
2574:
2572:Specific tests
2568:
2567:
2564:
2563:
2561:
2560:
2555:
2550:
2544:
2542:
2536:
2535:
2533:
2532:
2527:
2526:
2525:
2515:
2514:
2513:
2503:
2497:
2495:
2489:
2488:
2486:
2485:
2484:
2483:
2478:
2468:
2463:
2458:
2453:
2448:
2442:
2440:
2434:
2433:
2431:
2430:
2425:
2424:
2423:
2418:
2417:
2416:
2411:
2396:
2395:
2394:
2389:
2384:
2379:
2368:
2366:
2357:
2351:
2350:
2348:
2347:
2342:
2337:
2336:
2335:
2325:
2320:
2319:
2318:
2308:
2307:
2306:
2301:
2296:
2286:
2281:
2276:
2275:
2274:
2269:
2264:
2248:
2247:
2246:
2241:
2236:
2226:
2225:
2224:
2219:
2209:
2208:
2207:
2197:
2196:
2195:
2185:
2180:
2175:
2169:
2167:
2157:
2156:
2144:
2143:
2140:
2139:
2136:
2135:
2133:
2132:
2127:
2122:
2117:
2111:
2109:
2103:
2102:
2100:
2099:
2094:
2089:
2083:
2081:
2077:
2076:
2074:
2073:
2068:
2063:
2058:
2053:
2048:
2043:
2037:
2035:
2029:
2028:
2026:
2025:
2023:Standard error
2020:
2015:
2010:
2009:
2008:
2003:
1992:
1990:
1984:
1983:
1981:
1980:
1975:
1970:
1965:
1960:
1955:
1953:Optimal design
1950:
1945:
1939:
1937:
1927:
1926:
1914:
1913:
1910:
1909:
1906:
1905:
1903:
1902:
1897:
1892:
1887:
1882:
1877:
1872:
1867:
1862:
1857:
1852:
1847:
1842:
1837:
1832:
1826:
1824:
1818:
1817:
1815:
1814:
1809:
1808:
1807:
1802:
1792:
1787:
1781:
1779:
1773:
1772:
1770:
1769:
1764:
1759:
1753:
1751:
1750:Summary tables
1747:
1746:
1744:
1743:
1737:
1735:
1729:
1728:
1725:
1724:
1722:
1721:
1720:
1719:
1714:
1709:
1699:
1693:
1691:
1685:
1684:
1682:
1681:
1676:
1671:
1666:
1661:
1656:
1651:
1645:
1643:
1637:
1636:
1634:
1633:
1628:
1623:
1622:
1621:
1616:
1611:
1606:
1601:
1596:
1591:
1586:
1584:Contraharmonic
1581:
1576:
1565:
1563:
1554:
1544:
1543:
1531:
1530:
1528:
1527:
1522:
1516:
1513:
1512:
1505:
1504:
1497:
1490:
1482:
1476:
1475:
1473:. p. 141.
1466:
1457:
1439:(2): 163–172.
1425:
1415:(4): 313–318.
1401:
1391:(3): 255–259.
1375:
1372:
1369:
1368:
1344:
1326:
1308:
1297:juliastats.org
1284:
1261:
1260:
1258:
1255:
1254:
1253:
1245:
1242:
1241:
1240:
1234:
1212:
1206:
1200:
1193:JarqueBeraTest
1186:
1180:
1172:
1169:
1157:
1156:
1144:
1138:
1134:
1130:
1127:
1124:
1121:
1116:
1113:
1108:
1103:
1099:
1094:
1088:
1084:
1081:
1078:
1072:
1067:
1064:
1047:
1044:
1039:
1036:
1009:
1008:
1005:
1004:
1001:
998:
995:
992:
989:
985:
984:
981:
978:
975:
972:
969:
965:
964:
961:
958:
955:
952:
949:
945:
944:
941:
938:
935:
932:
929:
925:
924:
921:
918:
915:
912:
909:
874:and becomes a
830:asymptotically
804:
797:
794:
777:is the sample
763:
760:
731:
724:
721:
695:
688:
685:
670:
669:
658:
651:
646:
640:
636:
629:
626:
620:
615:
611:
607:
602:
597:
594:
591:
587:
581:
578:
572:
564:
560:
553:
550:
544:
539:
535:
531:
526:
521:
518:
515:
511:
505:
502:
494:
487:
480:
477:
468:
461:
458:
449:
446:
436:
425:
418:
414:
410:
405:
399:
395:
388:
385:
379:
374:
370:
366:
361:
356:
353:
350:
346:
340:
337:
331:
323:
319:
312:
309:
303:
298:
294:
290:
285:
280:
277:
274:
270:
264:
261:
253:
246:
239:
236:
227:
220:
217:
208:
205:
189:is the sample
181:is the sample
171:
170:
158:
152:
148:
144:
141:
138:
135:
130:
127:
122:
117:
113:
108:
102:
99:
94:
89:
86:
72:is defined as
67:test statistic
27:Normality test
26:
9:
6:
4:
3:
2:
3826:
3815:
3812:
3811:
3809:
3794:
3793:
3784:
3782:
3781:
3772:
3770:
3769:
3764:
3758:
3756:
3755:
3746:
3745:
3742:
3728:
3725:
3723:
3722:Geostatistics
3720:
3718:
3715:
3713:
3710:
3708:
3705:
3704:
3702:
3700:
3696:
3690:
3689:Psychometrics
3687:
3685:
3682:
3680:
3677:
3675:
3672:
3670:
3667:
3665:
3662:
3660:
3657:
3655:
3652:
3650:
3647:
3645:
3642:
3641:
3639:
3637:
3633:
3627:
3624:
3622:
3619:
3617:
3613:
3610:
3608:
3605:
3603:
3600:
3598:
3595:
3594:
3592:
3590:
3586:
3580:
3577:
3575:
3572:
3570:
3566:
3563:
3561:
3558:
3557:
3555:
3553:
3552:Biostatistics
3549:
3545:
3541:
3536:
3532:
3514:
3513:Log-rank test
3511:
3510:
3508:
3504:
3498:
3495:
3494:
3492:
3490:
3486:
3480:
3477:
3475:
3472:
3470:
3467:
3465:
3462:
3461:
3459:
3457:
3453:
3450:
3448:
3444:
3434:
3431:
3429:
3426:
3424:
3421:
3419:
3416:
3414:
3411:
3410:
3408:
3406:
3402:
3396:
3393:
3391:
3388:
3386:
3384:(Box–Jenkins)
3380:
3378:
3375:
3373:
3370:
3366:
3363:
3362:
3361:
3358:
3357:
3355:
3353:
3349:
3343:
3340:
3338:
3337:Durbin–Watson
3335:
3333:
3327:
3325:
3322:
3320:
3319:Dickey–Fuller
3317:
3316:
3314:
3310:
3304:
3301:
3299:
3296:
3294:
3293:Cointegration
3291:
3289:
3286:
3284:
3281:
3279:
3276:
3274:
3271:
3269:
3268:Decomposition
3266:
3265:
3263:
3259:
3256:
3254:
3250:
3240:
3237:
3236:
3235:
3232:
3231:
3230:
3227:
3223:
3220:
3219:
3218:
3215:
3213:
3210:
3208:
3205:
3203:
3200:
3198:
3195:
3193:
3190:
3188:
3185:
3183:
3180:
3179:
3177:
3175:
3171:
3165:
3162:
3160:
3157:
3155:
3152:
3150:
3147:
3145:
3142:
3140:
3139:Cohen's kappa
3137:
3136:
3134:
3132:
3128:
3124:
3120:
3116:
3112:
3108:
3103:
3099:
3085:
3082:
3080:
3077:
3075:
3072:
3070:
3067:
3066:
3064:
3062:
3058:
3052:
3048:
3044:
3038:
3036:
3033:
3032:
3030:
3028:
3024:
3018:
3015:
3013:
3010:
3008:
3005:
3003:
3000:
2998:
2995:
2993:
2992:Nonparametric
2990:
2988:
2985:
2984:
2982:
2978:
2972:
2969:
2967:
2964:
2962:
2959:
2957:
2954:
2953:
2951:
2949:
2945:
2939:
2936:
2934:
2931:
2929:
2926:
2924:
2921:
2919:
2916:
2915:
2913:
2911:
2907:
2901:
2898:
2896:
2893:
2891:
2888:
2886:
2883:
2882:
2880:
2878:
2874:
2870:
2863:
2860:
2858:
2855:
2854:
2850:
2846:
2830:
2827:
2826:
2825:
2822:
2820:
2817:
2815:
2812:
2808:
2805:
2803:
2800:
2799:
2798:
2795:
2794:
2792:
2790:
2786:
2776:
2773:
2769:
2763:
2761:
2755:
2753:
2747:
2746:
2745:
2742:
2741:Nonparametric
2739:
2737:
2731:
2727:
2724:
2723:
2722:
2716:
2712:
2711:Sample median
2709:
2708:
2707:
2704:
2703:
2701:
2699:
2695:
2687:
2684:
2682:
2679:
2677:
2674:
2673:
2672:
2669:
2667:
2664:
2662:
2656:
2654:
2651:
2649:
2646:
2644:
2641:
2639:
2636:
2634:
2632:
2628:
2626:
2623:
2622:
2620:
2618:
2614:
2608:
2606:
2602:
2600:
2598:
2593:
2591:
2586:
2582:
2581:
2578:
2575:
2573:
2569:
2559:
2556:
2554:
2551:
2549:
2546:
2545:
2543:
2541:
2537:
2531:
2528:
2524:
2521:
2520:
2519:
2516:
2512:
2509:
2508:
2507:
2504:
2502:
2499:
2498:
2496:
2494:
2490:
2482:
2479:
2477:
2474:
2473:
2472:
2469:
2467:
2464:
2462:
2459:
2457:
2454:
2452:
2449:
2447:
2444:
2443:
2441:
2439:
2435:
2429:
2426:
2422:
2419:
2415:
2412:
2410:
2407:
2406:
2405:
2402:
2401:
2400:
2397:
2393:
2390:
2388:
2385:
2383:
2380:
2378:
2375:
2374:
2373:
2370:
2369:
2367:
2365:
2361:
2358:
2356:
2352:
2346:
2343:
2341:
2338:
2334:
2331:
2330:
2329:
2326:
2324:
2321:
2317:
2316:loss function
2314:
2313:
2312:
2309:
2305:
2302:
2300:
2297:
2295:
2292:
2291:
2290:
2287:
2285:
2282:
2280:
2277:
2273:
2270:
2268:
2265:
2263:
2257:
2254:
2253:
2252:
2249:
2245:
2242:
2240:
2237:
2235:
2232:
2231:
2230:
2227:
2223:
2220:
2218:
2215:
2214:
2213:
2210:
2206:
2203:
2202:
2201:
2198:
2194:
2191:
2190:
2189:
2186:
2184:
2181:
2179:
2176:
2174:
2171:
2170:
2168:
2166:
2162:
2158:
2154:
2149:
2145:
2131:
2128:
2126:
2123:
2121:
2118:
2116:
2113:
2112:
2110:
2108:
2104:
2098:
2095:
2093:
2090:
2088:
2085:
2084:
2082:
2078:
2072:
2069:
2067:
2064:
2062:
2059:
2057:
2054:
2052:
2049:
2047:
2044:
2042:
2039:
2038:
2036:
2034:
2030:
2024:
2021:
2019:
2018:Questionnaire
2016:
2014:
2011:
2007:
2004:
2002:
1999:
1998:
1997:
1994:
1993:
1991:
1989:
1985:
1979:
1976:
1974:
1971:
1969:
1966:
1964:
1961:
1959:
1956:
1954:
1951:
1949:
1946:
1944:
1941:
1940:
1938:
1936:
1932:
1928:
1924:
1919:
1915:
1901:
1898:
1896:
1893:
1891:
1888:
1886:
1883:
1881:
1878:
1876:
1873:
1871:
1868:
1866:
1863:
1861:
1858:
1856:
1853:
1851:
1848:
1846:
1845:Control chart
1843:
1841:
1838:
1836:
1833:
1831:
1828:
1827:
1825:
1823:
1819:
1813:
1810:
1806:
1803:
1801:
1798:
1797:
1796:
1793:
1791:
1788:
1786:
1783:
1782:
1780:
1778:
1774:
1768:
1765:
1763:
1760:
1758:
1755:
1754:
1752:
1748:
1742:
1739:
1738:
1736:
1734:
1730:
1718:
1715:
1713:
1710:
1708:
1705:
1704:
1703:
1700:
1698:
1695:
1694:
1692:
1690:
1686:
1680:
1677:
1675:
1672:
1670:
1667:
1665:
1662:
1660:
1657:
1655:
1652:
1650:
1647:
1646:
1644:
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3664:Econometrics
3614: /
3597:Chemometrics
3574:Epidemiology
3567: /
3540:Applications
3382:ARIMA model
3329:Q-statistic
3278:Stationarity
3174:Multivariate
3117: /
3113: /
3111:Multivariate
3109: /
3049: /
3045: /
2819:Bayes factor
2718:Signed rank
2652:
2630:
2604:
2596:
2584:
2279:Completeness
2115:Cohort study
2013:Opinion poll
1948:Missing data
1935:Study design
1890:Scatter plot
1812:Scatter plot
1805:Spearman's ρ
1767:Grouped data
1470:
1461:
1436:
1432:
1412:
1408:
1388:
1384:
1360:. Retrieved
1356:
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1311:
1300:. Retrieved
1296:
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1275:. Retrieved
1265:
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1031:
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1010:
908:True α level
900:
890:
887:Type I error
882:
876:right-skewed
865:
862:
857:
825:
823:
671:
186:
178:
174:
172:
69:
64:
60:Anil K. Bera
35:
29:
3792:WikiProject
3707:Cartography
3669:Jurimetrics
3621:Reliability
3352:Time domain
3331:(Ljung–Box)
3253:Time-series
3131:Categorical
3115:Time-series
3107:Categorical
3042:(Bernoulli)
2877:Correlation
2857:Correlation
2653:Jarque–Bera
2625:Chi-squared
2387:M-estimator
2340:Asymptotics
2284:Sufficiency
2051:Interaction
1963:Replication
1943:Effect size
1900:Violin plot
1880:Radar chart
1860:Forest plot
1850:Correlogram
1800:Kendall's τ
1273:. MathWorks
1227:jarque.test
899:Calculated
50:matching a
3659:Demography
3377:ARMA model
3182:Regression
2759:(Friedman)
2720:(Wilcoxon)
2658:Normality
2648:Lilliefors
2595:Student's
2471:Resampling
2345:Robustness
2333:divergence
2323:Efficiency
2261:(monotone)
2256:Likelihood
2173:Population
2006:Stratified
1958:Population
1777:Dependence
1733:Count data
1664:Percentile
1641:Dispersion
1574:Arithmetic
1509:Statistics
1362:2017-10-26
1302:2020-02-04
1257:References
828:statistic
32:statistics
3040:Logistic
2807:posterior
2733:Rank sum
2481:Jackknife
2476:Bootstrap
2294:Bootstrap
2229:Parameter
2178:Statistic
1973:Statistic
1885:Run chart
1870:Pie chart
1865:Histogram
1855:Fan chart
1830:Bar chart
1712:L-moments
1599:Geometric
1339:R Project
1321:R Project
1126:−
1080:−
1034:-values.
836:with two
796:^
793:σ
762:¯
723:^
720:μ
687:^
684:μ
628:¯
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586:∑
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543:−
510:∑
479:^
476:σ
460:^
457:μ
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378:−
345:∑
311:¯
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238:^
235:σ
219:^
216:μ
140:−
3808:Category
3754:Category
3447:Survival
3324:Johansen
3047:Binomial
3002:Isotonic
2589:(normal)
2234:location
2041:Blocking
1996:Sampling
1875:Q–Q plot
1840:Box plot
1822:Graphics
1717:Skewness
1707:Kurtosis
1679:Variance
1609:Heronian
1604:Harmonic
1244:See also
1199:package.
819:variance
193: :
191:kurtosis
183:skewness
48:kurtosis
44:skewness
3780:Commons
3727:Kriging
3612:Process
3569:studies
3428:Wavelet
3261:General
2428:Plug-in
2222:L space
2001:Cluster
1702:Moments
1520:Outline
1453:1403192
1277:May 24,
1237:Wolfram
1231:moments
1223:tseries
1195:in the
1038:History
983:0.0168
943:0.1560
868:-values
3649:Census
3239:Normal
3187:Manova
3007:Robust
2757:2-way
2749:1-way
2587:-test
2258:
1835:Biplot
1626:Median
1619:Lehmer
1561:Center
1451:
1209:Python
1203:MATLAB
1177:ALGLIB
1159:where
1024:MATLAB
1017:Matlab
1003:0.002
1000:0.0012
997:0.0015
994:0.0033
991:0.0064
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963:0.062
951:0.1461
848:. The
832:has a
781:, and
672:where
173:where
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3273:Trend
2802:prior
2744:anova
2633:-test
2607:-test
2599:-test
2506:Power
2451:Pivot
2244:shape
2239:scale
1689:Shape
1669:Range
1614:Heinz
1589:Cubic
1525:Index
1449:JSTOR
1189:Julia
1183:gretl
988:0.01
980:0.016
977:0.020
971:0.051
960:0.067
957:0.079
954:0.109
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940:0.183
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3506:Test
2706:Sign
2558:Wald
1631:Mode
1569:Mean
1279:2009
928:0.1
923:100
842:test
779:mean
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65:The
58:and
46:and
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2681:AIC
1441:doi
1417:doi
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