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

Research output: Contribution to journalArticle

2 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 languageEnglish
Pages (from-to)53-60
Number of pages8
JournalStatistics and Probability Letters
Volume139
DOIs
Publication statusPublished - 1 Aug 2018

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Bernstein Function
Refinement
Evaluation
Integral

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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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The Lambert W function, Nuttall's integral, and the Lambert law. / Pakes, Anthony G.

In: Statistics and Probability Letters, Vol. 139, 01.08.2018, p. 53-60.

Research output: Contribution to journalArticle

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