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An inversion formula for a generalized transform

Published online by Cambridge University Press:  26 February 2010

J. G. Mauldon
J. G. Mauldon
Affiliation:
Corpus Christi College, Oxford.
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Extract

Let λ be a random variable with the distribution function F(λ). A transform of F which has, in effect, been used in several recent papers ([1], [2], [3], [4]; see also [6]) is

defined formally by the equation

It is the main purpose of this paper to prove the inversion formulae given in the two theorems below.

Type
Research Article
Information
Mathematika , Volume 4 , Issue 2 , December 1957 , pp. 146 - 155
Copyright
Copyright © University College London 1957

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References

1.Mauldon, J. G., Proc. Cambridge Phil. Soc., 047 (1951), 3312013;336.Google Scholar
2.Barton, D. E. and David, F. N., Mathematika, 002 (1955), 1502013;159.CrossRefGoogle Scholar
3.Barton, D. E. and David, F. N., Royal Statistical Soc. (B), 018 (1956), 79–94.Google Scholar
4.Barton, D. E. and David, F. N., Biometrika, 043 (1956), 104–112.Google Scholar
5.Widder, D. V., The Laplace Transform (Princeton, 1941).Google Scholar
6.Fox, C., Canadian Math. Journal, 009 (1957), 110–117.Google Scholar