Lambert's W, infinite divisibility and Poisson mixtures

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• 作者：Anthony G. Pakes^a ; ^{pakes@maths.uwa.edu.au}
• 关键词：Lambert W function ; Infinite divisibility ; Poisson mixtures ; Generalized convolutions ; Stable laws
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2011
• 出版时间：15 June 2011
• 年：2011
• 卷：378
• 期：2
• 页码：480-492
• 全文大小：203 K

文摘

The Lambert W function is shown to be the Laplace exponent of a positive infinitely divisible law (i.e. W is a Bernstein function) called the standard Lambert law. This law is a generalized gamma convolution. At least three Poisson mixture families are defined in terms of W. One of these is the generalized Poisson laws which are shown to be generalized negative-binomial convolutions. Mixing with positive stable laws yields further generalizations.