Alternative numerical computation of one-sided Levy and Mittag-Leffler distributions

Details Alternative numerical computation of one-sided Levy and Mittag-Leffler distributions Alternative numerical computation of one-sided Levy and Mittag-Leffler distributions

2011-06-02

arxiv.org/abs/1106.0531v2

Phys. Rev. E84, 026702 (2011)

Physics

Condensed Matter

Statistical Mechanics

6 pages, 5 figures. New references added, final version to appear in PRE. Numerical code available at http://vigo.ime.unicamp.

Scientific paper

10.1103/PhysRevE.84.026702

We consider here the recently proposed closed form formula in terms of the Meijer G-functions for the probability density functions $g_\alpha(x)$ of one-sided L\'evy stable distributions with rational index $\alpha=l/k$, with $0<\alpha<1$. Since one-sided L\'evy and Mittag-Leffler distributions are known to be related, this formula could also be useful for calculating the probability density functions $\rho_\alpha(x)$ of the latter. We show, however, that the formula is computationally inviable for fractions with large denominators, being unpractical even for some modest values of $l$ and $k$. We present a fast and accurate numerical scheme, based on an early integral representation due to Mikusinski, for the evaluation of $g_\alpha(x)$ and $\rho_\alpha(x)$, their cumulative distribution function and their derivatives for any real index $\alpha\in (0,1)$. As an application, we explore some properties of these probability density functions. In particular, we determine the location and value of their maxima as functions of the index $\alpha$. We show that $\alpha \approx 0.567$ and $\alpha \approx 0.605$ correspond, respectively, to the one-sided L\'evy and Mittag-Leffler distributions with shortest maxima. We close by discussing how our results can elucidate some recently described dynamical behavior of intermittent systems.

Affiliated with

Also associated with

No associations

Rating

Alternative numerical computation of one-sided Levy and Mittag-Leffler distributions 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 Alternative numerical computation of one-sided Levy and Mittag-Leffler distributions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Alternative numerical computation of one-sided Levy and Mittag-Leffler distributions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-222821