VII.—On Charlier's New Form of the Frequency Function

Author:

Aitken A. C.,Oppenheim A.

Abstract

It is known (cf. Charlier's statistical memoirs, passim) that the frequency function of Type A can be written compactly in symbolic form,where r! ar is equal to kr, the rth seminvariant of the distribution, D = d/dz andFor most purposes it is convenient to take the mean, k1 as origin and the standard deviation, as unit. The function of Type A then becomeswhere φ(x)=(2π)−½e−x2, and Ar is the coefficient of (−)rtr in the expansion of exp

Publisher

Cambridge University Press (CUP)

Subject

General Medicine,General Chemistry

Reference3 articles.

1. A Class of Reciprocal Functions

2. A New Form of the Frequency Function;Charlier;Meddelande Lunds Astr. Observ.,1928

3. Theory of Generating Functions and its Application to the Theory of Probability;Kameda;Journ. Fac. Sci. Imp. Univ. Tokyo,1925

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. V.—On the Orthogonal Polynomials in Frequencies of Type B;Proceedings of the Royal Society of Edinburgh;1933

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