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On Kendall-Ressel and related distributions. (English) Zbl 1232.60016

Author’s abstract: “We describe a connection of Kendall-Ressel and related laws with the lower real branch of the Lambert \(W\) function. A characterization of the canonical member of Kendall-Ressel class is found. The Letac-Mora interpretation of the reciprocity of two specific natural exponential families is extended by considering two related reproductive exponential dispersion models (EDMs). A local limit theorem on gamma convergence for the reproductive back-shifted Kendall-Ressel EDM is derived. Each member of this EDM is self-decomposable and unimodal, but not strongly unimodal. The coefficient of variation, skewness and kurtosis of each representative of this EDM are higher than the corresponding measures for the members of gamma and inverse Gaussian EDMs. An integral representation for the lower real branch of the Lambert \(W\) function is given.”
Reviewer: Miroslav M. Ristic

MSC:

60E07 Infinitely divisible distributions; stable distributions
60G51 Processes with independent increments; Lévy processes
60E05 Probability distributions: general theory
60F05 Central limit and other weak theorems
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References:

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