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.
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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 |
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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 |