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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. 22 pp. Ref. (Author)

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