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Biometrika 1977 64(2):401-409; doi:10.1093/biomet/64.2.401
© 1977 by Biometrika Trust
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On the null distribution of {surd}b1 for samples of size at most 25, with tables

H. P. MULHOLLAND*

*Present address: 20 St Leonard's Road, Exeter, Devon

For the sampling distribution of {surd}b1 in samples of size n from a normal parent, leading singular terms of the density fn at its singularities are obtained by application of a general method given previously. These terms are combined with correcting terms, fitted by moments, to give approximations to fn, integrals of which were used to compute a table of the distribution function Fn for 4 ≤ n ≤ 12: for l3 ≤ n ≤ 25 Gram-Charlier expansions were used. A recurrence for the moments of {surd}b1 is deduced from Geary's recurrence forfn. For 4 ≤ n ≤ 25 a table of percentage points is given.

Key Words: Moment • Percentage point • Recurrenoe formula • Singularity • Skewnees • Spline approximation • Test for normality


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