Some Utilizations of LambertWFunction in Distribution Theory

DOI10.1080/03610926.2011.602490zbMath1277.60035OpenAlexW1978364036MaRDI QIDQ2839066

Vladimir V. Vinogradov

Publication date: 4 July 2013

Published in: Communications in Statistics - Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03610926.2011.602490

zbMATH Keywords

infinite divisibilityPoisson approximationPoisson mixtureLambert \(W\) functionexponential dispersion modelunit variance functioncompound Poisson law\(\mathfrak L_{\gamma}\) distributionscompound exponential distributionconvolution and scaling closure propertiesextreme stable lawgeneralized Poisson familyinverse Gaussian approximationNeyman-type \(A\) familyreciprocal natural exponential familiessaddlepoint-type approximation

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Processes with independent increments; Lévy processes (60G51) Asymptotic distribution theory in statistics (62E20) Central limit and other weak theorems (60F05) Generalized linear models (logistic models) (62J12) Exact distribution theory in statistics (62E15) Probability distributions: general theory (60E05) Higher logarithm functions (33B30)

Related Items (2)

On Poisson-Tweedie mixtures ⋮ Analysis of over-dispersed count data with extra zeros using the Poisson log-skew-normal distribution

Cites Work

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• Natural real exponential families with cubic variance functions
• Domains of attraction to Tweedie distributions
• A hitting time for Lévy processes, with application to dams and branching processes
• On the Lambert \(w\) function
• A class of infinitely divisible distributions connected to branching processes and random walks
• On the Power-Variance Family of Probability Distributions
• Univariate Discrete Distributions
• Approximations to the Neyman Type A Distribution for Practical Problems

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