Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-25T02:14:33.023Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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