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

Axel Rossberg

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)531-541
Number of pages11
JournalJOURNAL OF APPLIED PROBABILITY
Volume45
Issue number2
Publication statusPublished - Jun 2008

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

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