Mixtures of Distributions, Moment Inequalities and Measures of Exponentiality and Normality

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Keilson, Julian and Sleutel, F.W. (1974) Mixtures of Distributions, Moment Inequalities and Measures of Exponentiality and Normality. Annals of Probability, 2 (1). pp. 112-130. ISSN 0091-1798

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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 $\mathscr{D}$ containing most of the classical distributions as well as the passage time densities $s_{mn}(\tau)$ for arbitrary birth-death processes.
Item Type:Article
Copyright:© 1974 Institute of Mathematical Statistics
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/70392
Official URL:http://dx.doi.org/10.1214/aop/1176996756
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