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On Extreme Stable Laws and Some Applications

Author: Eaton, Morris L..
Author: Morris, Carl
Author: Rubin, Herman
Corporate Author: RAND Corporation
Corporate Report Number: R-551-PR
Date of Publication: 1971-02
Pages: 24
Contract: F44620-67-C-0045
Project: Project RAND
AD Number: AD0720799

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, exp (cz log z), is a moment-generating function is used to establish two interesting statistical results: first, that exp (r log r) 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.

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