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Mittag-Leffler random number generator

version (2.29 KB) by Guido Germano
Generates a matrix of Mittag-Leffler pseudo-random numbers


Updated 04 Apr 2016

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Returns a matrix of IID random numbers distributed according to the one-parameter Mittag-Leffler distribution with index (or exponent) beta and scale parameter gamma_t. The size of the returned matrix is the same as that of the input matrices beta and gamma_t, that must match. Alternatively, if beta and gamma_t are scalars, mlrnd(beta, gamma_t, m) returns an m by m matrix, and mlrnd(beta, gamma_t, m, n) returns an m by n matrix.
[1] T. J. Kozubowski and S. T. Rachev, "Univariate geometric stable laws", Journal of Computational Analysis and Applications 1, 177-219 (1999).
[2] D. Fulger, E. Scalas, G. Germano, "Monte Carlo simulation of uncoupled continuous-time random walks yielding a stochastic solution of the space-time fractional diffusion equation", Physical Review E 77, 021122 (2008).

Comments and Ratings (4)

Guido Germano

Please read carefully the overview, the function and the references, in particular Ref. 2, Fig. 2 and Eqs. (9), (10) and (18). This function provides random numbers with the one-parameter Mittag-Leffler CCDF E_\beta(-t^\beta) (if the scaling factor \gamma = 1), or if you prefer E_\alpha(-t^\alpha). The second parameter of the two-parameter Mittag-Leffler function is set to 1. Notice the difference between Mittag-Leffler function and Mittag-Leffler distribution.

wanli wang

here the Mittag-Leffler function is E_{alpha,beta}(-t) how to generate E_{alpha,beta}(-t^\alpha) ? is there some relation between them??

Hongguang Sun

Very good, thanks for your effort.

Martin Eisenacher

Exactly that I missed for years!


Added a comment to one line of code, corrected the format of reference 1

Associated an open source BSD licence to this submission, as recommended by John Kelly, the Administrator of Matlab Central's File Exchange

Small change to the summary

Small corrections to the description and the tags

Changed title and added references to description.

MATLAB Release Compatibility
Created with R2007b
Compatible with any release
Platform Compatibility
Windows macOS Linux

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