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

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An Erratum to this article was published on 01 April 2014

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.

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Authors and Affiliations

  1. Department of Mathematics, Ohio University, Athens, OH, 45701, USA

    Vladimir Vinogradov

  2. School of Computing, Engineering and Applied Mathematics, University of Abertay Dundee, Dundee, DD1 1HG, UK

    Richard B. Paris

  3. Institute of Mathematics and Informatics, Vilnius University, Akademijos 4, LT-08663, Vilnius, Lithuania

    Olga Yanushkevichiene

Authors
  1. Vladimir Vinogradov
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  2. Richard B. Paris
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  3. Olga Yanushkevichiene
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Correspondence to Vladimir Vinogradov.

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An erratum to this article is available at http://dx.doi.org/10.1007/s10986-014-9240-1.

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Vinogradov, V., Paris, R.B. & Yanushkevichiene, O. New properties and representations for members of the power-variance family. II. Lith Math J 53, 103–120 (2013). https://doi.org/10.1007/s10986-013-9197-5

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