New properties and representations for members of the power-variance family. II

Vladimir Vinogradov, Richard B. Paris, Olga Yanushkevichiene

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    7 Citations (Scopus)
    120 Downloads (Pure)

    Abstract

    This is the continuation of [V. Vinogradov, R.B. Paris, and O. Yanushkevichiene, New properties and representations for members of the power-variance family. I, Lith. Math. J., 52(4):444–461, 2012]. Members of the powervariance family of distributions became popular in stochastic modeling which necessitates a further investigation of their properties. Here, we establish Zolotarev duality of the refined saddlepoint-type approximations for all members of this family, thereby providing an interpretation of the Letac–Mora reciprocity of the corresponding NEFs. Several illustrative examples are given. Subtle properties of related special functions are established.

    An erratum to this article is available at 10.1007/s10986-014-9240-1.
    Original languageEnglish
    Pages (from-to)103-120
    Number of pages18
    JournalLithuanian Mathematical Journal
    Volume53
    Issue number1
    DOIs
    Publication statusPublished - Jan 2013

    Keywords

    • Poincaré series
    • Difference quotient
    • Poisson-gamma laws
    • Reciprocity
    • Refined saddlepoint approximations
    • Stable laws
    • Stokes phenomenon
    • Wright function
    • Zolotarev duality

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