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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

[1] Barlow, R., Marshall, A. and Proschan, F. (1963) Properties of probability distributions with monotone hazard rate. Ann. Math. Statist. 34, 375–389.Google Scholar
[2] Gnedenko, B. and Kolmogorov, A. N. (1954) Limit Distributions for Sums of Independent Random Variables. Addison-Wesley, Cambridge, Mass.Google Scholar
[3] Loève, M. (1960) Probability Theory. D. Van Nostrand Co., New York.Google Scholar
[4] Mandelbrot, M. B. (1959) Variables et processus stochastiques de Pareto-Lévy, et la répartition des revenus. Académie des Sciences 249, 2153–2155.Google Scholar
[5] Widder, D. V. (1941) The Laplace Transform. Princeton University Press, Princeton, New Jersey.Google Scholar
[6] Zolotarev, V. M. (1961) On analytic properties of stable distribution laws. Selected Translations Math. Statist. Prob. 1, 207–211.Google Scholar