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

Vladimir Vinogradov; Richard B. Paris; Olga Yanushkevichiene

doi:10.1007/s10986-013-9197-5

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 language	English
Pages (from-to)	103-120
Number of pages	18
Journal	Lithuanian Mathematical Journal
Volume	53
Issue number	1
DOIs	https://doi.org/10.1007/s10986-013-9197-5
Publication status	Published - 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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New properties and representations for members of the power-variance family. II

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Keywords

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