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

Fulger, D; Scalas, E; Germano, G; (2013) Random numbers from the tails of probability distributions using the transformation method. Fractional Calculus and Applied Analysis , 16 (2) pp. 332-353. 10.2478/s13540-013-0021-z. Green open access

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Abstract

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.

Type: Article
Title: Random numbers from the tails of probability distributions using the transformation method
Open access status: An open access version is available from UCL Discovery
DOI: 10.2478/s13540-013-0021-z
Publisher version: http://dx.doi.org/10.2478/s13540-013-0021-z
Language: English
Additional information: Copyright © 2013 by Walter de Gruyter GmbH.
Keywords: random number generation, alpha-stable distribution, Mittag-Leffler distribution, fractional diffusion
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/1407445
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