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

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

2010-05-14

arxiv.org/abs/1005.2614v1

Mathematics

Probability

24 pages, 7 figures, 1 table

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Technique for computing the PDFs and CDFs of non-negative infinitely divisible random variables does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Technique for computing the PDFs and CDFs of non-negative infinitely divisible random variables, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Technique for computing the PDFs and CDFs of non-negative infinitely divisible random variables will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-520434