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 | |
| Publication status | Published - 1 Aug 2018 |
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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 journal › Article
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
VL - 139
SP - 53
EP - 60
JO - Statistics & Probability Letters
JF - Statistics & Probability Letters
SN - 0167-7152
ER -