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February, 1974 Mixtures of Distributions, Moment Inequalities and Measures of Exponentiality and Normality
Julian Keilson, F. W. Steutel
Ann. Probab. 2(1): 112-130 (February, 1974). DOI: 10.1214/aop/1176996756

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 $\mathscr{D}$ containing most of the classical distributions as well as the passage time densities $s_{mn}(\tau)$ for arbitrary birth-death processes.

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Julian Keilson. F. W. Steutel. "Mixtures of Distributions, Moment Inequalities and Measures of Exponentiality and Normality." Ann. Probab. 2 (1) 112 - 130, February, 1974. https://doi.org/10.1214/aop/1176996756

Information

Published: February, 1974
First available in Project Euclid: 19 April 2007

zbMATH: 0325.60019
MathSciNet: MR356180
Digital Object Identifier: 10.1214/aop/1176996756

Subjects:
Primary: 60E05
Secondary: 60F05 , 60J80

Keywords: birth-death processes , completely monotone densities , Log-concavity , Log-convexity , measures of exponentiality and normality , Mixtures of distributions , Moment inequalities , sojourn times , total positivity , weak convergence

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 1 • February, 1974
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