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Biometrika 1983 70(1):227-234; doi:10.1093/biomet/70.1.227
© 1983 by Biometrika Trust
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Distribution of the kurtosis statistic b2 for normal samples

F. J. ANSCOMBE and WILLIAM J. GLYNN

Department of Statistics, Yale University New Haven, Connecticut, U.S.A.
Department of Statistics, Harvard University Cambridge, Massachusetts, U.S.A.

D'Agostino & Pearson (1973) gave percentage points of the distribution of b2 for independent observations from a common univariate normal distribution. Their results can be adequately approximated, when the first three moments of the distribution of b2 have been determined, by fitting a linear function of the reciprocal of a X2 variable and then using the Wilson-Hilferty transformation. Evidence is presented suggesting that the same method of approximation is satisfactory for the b2 statistic calculated from any set of linear-least-squares residuals, on the hypothesis of normal homoscedastic errors.

Key Words: b2 statistic • Kurtosis • Pearson type V distribution • Residuals


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