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

Fulger, Daniel, Scalas, Enrico and Germano, Guido (2013) Random numbers from the tails of probability distributions using the transformation method. Fractional Calculus and Applied Analysis, 16 (2). pp. 332-353. ISSN 1311-0454

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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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics
Depositing User: Enrico Scalas
Date Deposited: 24 Sep 2014 05:53
Last Modified: 24 Sep 2014 05:53
URI: http://sro.sussex.ac.uk/id/eprint/50236
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