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

DOI10.1007/s10986-012-9186-0zbMath1284.60040OpenAlexW2029898465MaRDI QIDQ1936260

Vladimir V. Vinogradov, O. L. Yanushkyavichene, Richard B. Paris

Publication date: 21 February 2013

Published in: Lithuanian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://rke.abertay.ac.uk/en/publications/02bedb31-d3de-47f5-af3a-e9d5f38a0d83

zbMATH Keywords

Poincaré seriesstable lawsreciprocitydifference quotientWright functionStokes phenomenonPoisson-gamma lawsrefined saddle-point approximationsZolotarev duality

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Asymptotic distribution theory in statistics (62E20) Characteristic functions; other transforms (60E10) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Characterization and structure theory of statistical distributions (62E10) Large deviations (60F10) Other functions defined by series and integrals (33E20) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15)

Related Items (6)

Asymptotic and structural properties of special cases of the Wright function arising in probability theory ⋮ New properties and representations for members of the power-variance family. II ⋮ On Poisson-Tweedie mixtures ⋮ On the mean value parametrization of natural exponential families -- a revisited review ⋮ Exponentially small expansions of the Wright function on the Stokes lines ⋮ Erratum to: ``New properties and representations for members of the power-variance family. II

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