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

    Fingerprint

    Moment Inequalities
    Mixture of Distributions
    Normality
    Product-moment correlation
    Passage Time
    Scale Mixture
    Birth-death Process
    Kurtosis
    Limit Theorems
    Central limit theorem
    Metric space
    Arbitrary
    Moment inequalities
    Mixture of distributions
    Limit theorems
    Coefficients

    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

    Cite this

    Keilson, Julian ; Sleutel, F.W. / Mixtures of Distributions, Moment Inequalities and Measures of Exponentiality and Normality. In: Annals of probability. 1974 ; Vol. 2, No. 1. pp. 112-130.
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    Mixtures of Distributions, Moment Inequalities and Measures of Exponentiality and Normality. / Keilson, Julian; Sleutel, F.W.

    In: Annals of probability, Vol. 2, No. 1, 1974, p. 112-130.

    Research output: Contribution to journalArticleAcademic

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    T1 - Mixtures of Distributions, Moment Inequalities and Measures of Exponentiality and Normality

    AU - Keilson, Julian

    AU - Sleutel, F.W.

    PY - 1974

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    N2 - 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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    KW - log-concavity

    KW - log-convexity

    KW - completely monotone densities

    KW - total positivity

    KW - measures of exponentiality and normality

    KW - sojourn times

    KW - moment inequalities

    KW - Birth-death processes

    KW - Mixtures of distributions

    KW - IR-70392

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