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Random numbers from the tails of probability distributions using the transformation method

journal contribution
posted on 2023-06-08, 18:24 authored by Daniel Fulger, Enrico Scalas, Guido Germano
The speed of many one-line transformation methods for the production of, for example, Lévy alpha-stable random numbers, which generalize Gaussian ones, and Mittag-Leffler random numbers, which generalize exponential ones, is very high and satisfactory for most purposes. However, fast rejection techniques like the ziggurat by Marsaglia and Tsang promise a significant speed-up for the class of decreasing probability densities, if it is possible to complement them with a method that samples the tails of the infinite support. This requires the fast generation of random numbers greater or smaller than a certain value. We present a method to achieve this, and also to generate random numbers within any arbitrary interval. We demonstrate the method showing the properties of the transformation maps of the above mentioned distributions as examples of stable and geometric stable random numbers used for the stochastic solution of the space-time fractional diffusion equation.

History

Publication status

  • Published

Journal

Fractional Calculus and Applied Analysis

ISSN

1311-0454

Publisher

Springer Verlag

Issue

2

Volume

16

Page range

332-353

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2014-09-24

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