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

Published online by Cambridge University Press:  15 September 2014

A. C. Aitken  and
A. Oppenheim
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Extract

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 and

For most purposes it is convenient to take the mean, k1 as origin and the standard deviation, as unit. The function of Type A then becomes

where φ(x)=(2π)−½e−x2, and Ar is the coefficient of (−)rtr in the expansion of exp

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 51 , 1932 , pp. 35 - 41
Copyright
Copyright © Royal Society of Edinburgh 1932

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References

REFERENCES

Charlier, C. V. L., Meddelande Lunds Astr. Observ., 2, 51 (1928), “A New Form of the Frequency Function.”Google Scholar
Kameda, T., Journ. Fac. Sci. Imp. Univ. Tokyo, 1 1 (1), (1925), “Theory of Generating Functions and its Application to the Theory of Probability,” pp. 1–62, and specially 31–36.Google Scholar
Hille, E., Annals of Math., 2, 27 (1926), “A Class of Reciprocal Functions,” pp. 427–464, and specially 457–464.CrossRefGoogle Scholar