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Some applications of Mellin transforms to the theory of bivariate statistical distributions*

Published online by Cambridge University Press:  24 October 2008

Charles Fox
Charles Fox
Affiliation:
McGill University Montreal
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Abstract

A method is described for finding the frequency functions of bivariate random variables which are the products or ratios of other bivariate random variables. If (ξ, n) are a pair of bivariate random variables with joint frequency function f(x, y) then the method depends upon the fact that the expectation of │ ξ │r–1│η│s–1 is related to the Mellin transform of f(x, y) in two dimensions. Knowing the expectation we can then recover the frequency function by means of the inverse Mellin transform. Some examples are given to illustrate the theory.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 53 , Issue 3 , July 1957 , pp. 620 - 628
Copyright
Copyright © Cambridge Philosophical Society 1957

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References

REFERENCES

(1)Cramer, H., Mathematical methods of statistics (Princeton, 1945).Google Scholar
(2)Epstein, B., Some applications of the Mellin transform in statistics. Ann. Math. Statist, 20 (1948), 370–9.CrossRefGoogle Scholar
(3)Forsyth, A. R.The theory of functions of two complex variables (Cambridge, 1914).Google Scholar
(4)Reed, I. S.The Mellin type of double integral. Duke Math. J. 11 (1944), 565–72.Google Scholar
(5)Saks, S., Theory of the integral (Warsaw, 1935).Google Scholar
(6)Titchmarsh, E. C.Theory of Fourier Integrals (Oxford, 1937).Google Scholar
(7)Whittaker, E. T. and Watson, G. N.A course of modern analysis (Cambridge, 1920).Google Scholar