Abstract
We present a method for computing the probability density function (PDF) and the cumulative distribution function (CDF) of a nonnegative infinitely divisible random variable X. Our method uses the Lévy-Khintchine representation of the Laplace transform Ee-λX = e-ϕ(λ), where ϕ is the Laplace exponent. We apply the Post-Widder method for Laplace transform inversion combined with a sequence convergence accelerator to obtain accurate results. We demonstrate this technique on several examples, including the stable distribution, mixtures thereof, and integrals with respect to nonnegative Lévy processes.
Citation
Mark S. Veillette. Murad S. Taqqu. "A technique for computing the PDFs and CDFs of nonnegative infinitely divisible random variables." J. Appl. Probab. 48 (1) 217 - 237, March 2011. https://doi.org/10.1239/jap/1300198146
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