Technique for computing the PDFs and CDFs of non-negative infinitely divisible random variables

Autor:	Veillette, Mark S., Taqqu, Murad S.
Rok vydání:	2010
Předmět:	Mathematics - Probability Mathematics - Numerical Analysis 60E07 (Primary) 65C50 6008 6004 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We present a method for computing the PDF and CDF of a non-negative infinitely divisible random variable $X$. Our method uses the L\'{e}vy-Khintchine representation of the Laplace transform $\mathbb{E} e^{-\lambda X} = e^{-\phi(\lambda)}$, where $\phi$ 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 non-negative L\'{e}vy processes. Software to implement this method is available from the authors and we illustrate its use at the end of the paper. Comment: 24 pages, 7 figures, 1 table
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1005.2614 Zobrazit plný text záznamu View this record from Arxiv