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

6 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

Access to Document

10.1016/j.spl.2018.03.015

Cite this

@article{22ab0bbd4cd54841a90c190074ecb1e1,

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

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.",

keywords = "Bernstein function, Infinite divisibility, Lambert W function",

author = "Pakes, {Anthony G.}",

year = "2018",

month = aug,

day = "1",

doi = "10.1016/j.spl.2018.03.015",

language = "English",

volume = "139",

pages = "53--60",

journal = "Statistics and Probability Letters",

issn = "0167-7152",

publisher = "Elsevier",

}

TY - JOUR

T1 - The Lambert W function, Nuttall's integral, and the Lambert law

AU - Pakes, Anthony G.

PY - 2018/8/1

Y1 - 2018/8/1

N2 - 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.

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.

KW - Bernstein function

KW - Infinite divisibility

KW - Lambert W function

UR - http://www.scopus.com/inward/record.url?scp=85045241014&partnerID=8YFLogxK

U2 - 10.1016/j.spl.2018.03.015

DO - 10.1016/j.spl.2018.03.015

M3 - Article

AN - SCOPUS:85045241014

SN - 0167-7152

VL - 139

SP - 53

EP - 60

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

ER -

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

Abstract

Access to Document

Other files and links

Fingerprint

Cite this