Lambert's \(W\), infinite divisibility and Poisson mixtures

DOI10.1016/j.jmaa.2011.01.066zbMath1223.60016OpenAlexW2077522371MaRDI QIDQ633650

Anthony G. Pakes

Publication date: 29 March 2011

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.01.066

zbMATH Keywords

stable lawsinfinite divisibilityLambert \(W\) functionPoisson mixturesgeneralized convolutions

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Characteristic functions; other transforms (60E10) Sums of independent random variables; random walks (60G50)

Related Items

Stieltjes and other integral representations for functions of LambertW, The Lambert \(W\) function, Nuttall's integral, and the Lambert law, Transcendental equations in the Schwinger-Keldysh nonequilibrium theory and nonvanishing correlations, New families of subordinators with explicit transition probability semigroup, Geometric branching reproduction Markov processes, Self-decomposable laws from continuous branching processes, Derivatives of the tree function, Some Utilizations of LambertWFunction in Distribution Theory, On some compound distributions with Borel summands, Bernstein, Pick, Poisson and related integral expressions for LambertW

Cites Work

• A hitting time for Lévy processes, with application to dams and branching processes
• On the Lambert \(w\) function
• Poisson mixtures and quasi-infinite divisibility of distributions
• Some applications of the Lambert W function to classical statistical mechanics
• Generalized Poisson Distribution: the Property of Mixture of Poisson and Comparison with Negative Binomial Distribution
• The Borel-Tanner distribution
• Bernstein functions. Theory and applications
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