The Lambert W function, Nuttall's integral, and the Lambert law

Anthony G. Pakes

doi:10.1016/j.spl.2018.03.015

The Lambert W function, Nuttall's integral, and the Lambert law

Anthony G. Pakes

School of Physics, Mathematics and Computing

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

This paper offers a new proof that the principal Lambert W-function W(s) is a Bernstein function. The proof derives from a known integral evaluation and leads to a more detailed description of W(s) as a Thorin–Bernstein function with a real-variable description of the Thorin measure, and refinements of some known properties of the Lambert distribution.

Original language	English
Pages (from-to)	53-60
Number of pages	8
Journal	Statistics and Probability Letters
Volume	139
DOIs	https://doi.org/10.1016/j.spl.2018.03.015
Publication status	Published - 1 Aug 2018

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abstract = "This paper offers a new proof that the principal Lambert W-function W(s) is a Bernstein function. The proof derives from a known integral evaluation and leads to a more detailed description of W(s) as a Thorin–Bernstein function with a real-variable description of the Thorin measure, and refinements of some known properties of the Lambert distribution.",

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AB - This paper offers a new proof that the principal Lambert W-function W(s) is a Bernstein function. The proof derives from a known integral evaluation and leads to a more detailed description of W(s) as a Thorin–Bernstein function with a real-variable description of the Thorin measure, and refinements of some known properties of the Lambert distribution.

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KW - Infinite divisibility

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DO - 10.1016/j.spl.2018.03.015

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SP - 53

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JO - Statistics & Probability Letters

JF - Statistics & Probability Letters

SN - 0167-7152

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The Lambert W function, Nuttall's integral, and the Lambert law

Abstract

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