Mixtures of distributions, moment inequalities and measures of exponentiality and normality

J. Keilson, F.W. Steutel

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Abstract

The central limit theorem and limit theorems for rarity require measures of normality and exponentiality for their implementation. Simple useful measures are exhibited for these in a metric space setting, obtained from inequalities for scale mixtures and power mixtures. It is shown that the Pearson coefficient of Kurtosis is such a measure for normality in a broad class D containing most of the classical distributions as well as the passage time densities s{mn}(tau) for arbitrary birth-death processes.
Original languageEnglish
Pages (from-to)112-130
Number of pages19
JournalThe Annals of Probability
Volume2
Issue number1
DOIs
Publication statusPublished - 1974

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