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On extreme stable laws and some applications

Published online by Cambridge University Press:  14 July 2016

Morris L. Eaton ,
Carl Morris  and
Herman Rubin
Morris L. Eaton
Affiliation:
University of Chicago
Carl Morris
Affiliation:
The Rand Corporation, Santa Monica, California
Herman Rubin
Affiliation:
Purdue University, Lafayette, Indiana
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Summary

It is shown that the extreme stable laws have one-sided moment generating functions with interesting mathematical forms. The fact that one of these forms, zcz, is a moment generating function is used to establish two interesting statistical results; first, that rr is a moment sequence for a density with decreasing failure rate, and secondly, that the likelihood ratio test for testing a simple null hypothesis in a multinomial distribution is admissible and Bayes.

Type
Research Papers
Information
Journal of Applied Probability , Volume 8 , Issue 4 , December 1971 , pp. 794 - 801
Copyright
Copyright © Applied Probability Trust 1971 

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References

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