On the Laplace Transform of the Lognormal Distribution



Asmussen, Soren, Jensen, Jens Ledet and Rojas-Nandayapa, Leonardo ORCID: 0000-0001-5652-3183
(2016) On the Laplace Transform of the Lognormal Distribution. Methodology and Computing in Applied Probability, 18 (2). pp. 441-458.

[img] Text
LapLogRev08.pdf - Author Accepted Manuscript

Download (592kB)

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 ~(

Item Type: Article
Uncontrolled Keywords: Characteristic function, Efficiency, Importance sampling, Lambert W function, Laplace transform, Laplace's method, Lognormal distribution, Moment generating function, Monte Carlo method, Rare event simulation
Depositing User: Symplectic Admin
Date Deposited: 11 Dec 2017 08:36
Last Modified: 19 Jan 2023 06:48
DOI: 10.1007/s11009-014-9430-7
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3013892