Laplace transforms of probability distributions and their inversions are easy on logarithmic scales

Rossberg AG (2008). Laplace transforms of probability distributions and their inversions are easy on logarithmic scales. Journal of Applied Probability 45 (2): 531-541. DOI:10.1239/jap/1214950365.

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Abstract

It is shown that, when expressing arguments in terms of their logarithms, the Laplace transform of a function is related to the antiderivative of this function by a simple convolution. This allows efficient numerical computations of moment generating functions of positive random variables and their inversion. The application of the method is straightforward, apart from the necessity to implement it using high-precision arithmetics. In numerical examples the approach is demonstrated to be particularly useful for distributions with heavy tails, such as lognormal, Weibull, or Pareto distributions, which are otherwise difficult to handle. The computational efficiency compared to other methods is demonstrated for an M/G/1 queueing problem.

Item Type: Article
Uncontrolled Keywords: Moment generating function; Laplace transform; Transform inversion; Heavy tail
Research Programs: Evolution and Ecology (EEP)
Bibliographic Reference: Journal of Applied Probability; 45(2):531-541 (June 2008)
Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 08:41
Last Modified: 26 Aug 2016 08:22
URI: http://pure.iiasa.ac.at/8566

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