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

Julian Keilson, F.W. Sleutel

    Research output: Contribution to journalArticleAcademic

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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.
    Original languageEnglish
    Pages (from-to)112-130
    JournalAnnals of probability
    Volume2
    Issue number1
    DOIs
    Publication statusPublished - 1974

    Keywords

    • Weak convergence
    • log-concavity
    • log-convexity
    • completely monotone densities
    • total positivity
    • measures of exponentiality and normality
    • sojourn times
    • moment inequalities
    • Birth-death processes
    • Mixtures of distributions
    • IR-70392

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