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Biometrika 1973 60(1):169-173; doi:10.1093/biomet/60.1.169
© 1973 by Biometrika Trust
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Approaches to the null distribution of {surd} b1

RALPH B. D'AGOSTINO1 and GARY L. TIETJEN2

1Boston University
2Los Alamos Scientific Laboratory

A comparative study of approximations to the null distribution of {surd} b1 is given for small sample sizes, i. e. n ≤ 35. The approximations studied are the approximations by the normal distribution, the Johnson SU distributions, the t or Pearson Type VII distributions, the Cornish-Fisher expansions using moments up to the eighth, with and without Geary's adjustment, and, finally, Monte-Carlo simulations. For the usual levels of significance all the approximations, except the normal approximation, appear satisfactory for n ≥ 8. Because the SU and t distributions allow approximations to the probability integrals, they can be used to combine the results of independently drawn samples.

Key Words: Tests of normality • Measure of skewness • Johnson's approximation • t approximation • Pearson curves approximation • Cornish-Fisher expansions • Simulation • Monte-Carlo procedure


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