On two extensions of the canonical Feller–Spitzer distribution

Vladimir Vladimirovich Vinogradov*, Richard Bruce Paris

*Corresponding author for this work

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    Abstract

    We introduce two extensions of the canonical Feller–Spitzer distribution from the class of Bessel densities, which comprise two distinct stochastically decreasing one-parameter families of positive absolutely continuous infinitely divisible distributions with monotone densities, whose upper tails exhibit a power decay. The densities of the members of the first class are expressed in terms of the modified Bessel function of the first kind, whereas the members of the second class have the densities of their Lévy measure given by virtue of the same function. The Laplace transforms for both these families possess closed–form representations in terms of specific hypergeometric functions. We obtain the explicit expressions by virtue of the particular parameter value for the moments of the distributions considered and establish the monotonicity of the mean, variance, skewness and excess kurtosis within the families. We derive numerous properties of members of these classes by employing both new and previously known properties of the special functions involved and determine the variance function for the natural exponential family generated by a member of the second class.
    Original languageEnglish
    Article number3
    Number of pages25
    JournalJournal of Statistical Distributions and Applications
    Volume8
    Issue number1
    Early online date4 Mar 2021
    DOIs
    Publication statusE-pub ahead of print - 4 Mar 2021
    Event3rd International Conference on Statistical Distributions and Applications - Eberhard Conference Center, Grand Rapids, United States
    Duration: 10 Oct 201912 Oct 2019
    Conference number: 3rd
    http://people.cst.cmich.edu/lee1c/icosda2019/index.htm

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