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June, 1957 An Approximate Formula for the Cumulative $z$-Distribution
John Wishart
Ann. Math. Statist. 28(2): 504-510 (June, 1957). DOI: 10.1214/aoms/1177706980


A straightforward expansion and integration of the frequency function for Fisher's $z$ produces a formula for the probability that $z$ is not exceeded, of which the successive terms decrease rapidly when $n_1$ and $n_2$ are large. It is given in terms of incomplete normal moment functions (or $\chi^2$ probabilities), and as a polynomial in $zN^{1/2}$, where $N$ is the harmonic mean of $n_1$ and $n_2$. This last form is identical with the inverted Cornish-Fisher expansion, originally deduced by quite different methods.


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John Wishart. "An Approximate Formula for the Cumulative $z$-Distribution." Ann. Math. Statist. 28 (2) 504 - 510, June, 1957.


Published: June, 1957
First available in Project Euclid: 27 April 2007

zbMATH: 0082.13505
MathSciNet: MR88119
Digital Object Identifier: 10.1214/aoms/1177706980

Rights: Copyright © 1957 Institute of Mathematical Statistics

Vol.28 • No. 2 • June, 1957
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