On the laplace transform of the lognormal distribution

Asmussen, Søren, Jensen, Jens Ledet and Rojas-Nandayapa, Leonardo (2016) On the laplace transform of the lognormal distribution. Methodology and Computing in Applied Probability, 18 2: 441-458. doi:10.1007/s11009-014-9430-7

Author Asmussen, Søren
Jensen, Jens Ledet
Rojas-Nandayapa, Leonardo
Title On the laplace transform of the lognormal distribution
Journal name Methodology and Computing in Applied Probability   Check publisher's open access policy
ISSN 1573-7713
Publication date 2016-06-01
Year available 2016
Sub-type Article (original research)
DOI 10.1007/s11009-014-9430-7
Open Access Status Not Open Access
Volume 18
Issue 2
Start page 441
End page 458
Total pages 18
Place of publication New York, NY United States
Publisher Elsevier
Collection year 2017
Language eng
Formatted abstract
Integral transforms of the lognormal distribution are of great importance in statistics and probability, yet closed-form expressions do not exist. A wide variety of methods have been employed to provide approximations, both analytical and numerical. In this paper, we analyse a closed-form approximation L˜(θ) of the Laplace transform L(θ) which is obtained via a modified version of Laplace’s method. This approximation, given in terms of the Lambert W(⋅) function, is tractable enough for applications. We prove that ~(𝜃) is asymptotically equivalent to ℒ(𝜃) as 𝜃 → ∞. We apply this result to construct a reliable Monte Carlo estimator of ℒ(𝜃) and prove it to be logarithmically efficient in the rare event sense as 𝜃 → ∞.
Keyword Characteristic function
Importance sampling
Lambert W function
Laplace transform
Laplace’s method
Lognormal distribution
Moment generating function
Monte Carlo method
Rare event simulation
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
HERDC Pre-Audit
Version Filter Type
Citation counts: TR Web of Science Citation Count  Cited 1 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 1 times in Scopus Article | Citations
Google Scholar Search Google Scholar
Created: Tue, 10 May 2016, 00:21:58 EST by System User on behalf of School of Mathematics & Physics