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

Vladimir Vinogradov, Richard B. Paris, Olga Yanushkevichiene

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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

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