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Random numbers from the tails of probability distributions using the transformation method
The speed of many one-line transformation methods for the production of, for
example, Levy 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, for the class of decreasing
probability densities fast rejection implementations like the Ziggurat by
Marsaglia and Tsang promise a significant speed-up 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 transform 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.Comment: 17 pages, 7 figures, submitted to a peer-reviewed journa
Scientific Endeavors of A.M. Mathai: An Appraisal on the Occasion of his Eightieth Birthday, April 2015
A.M. Mathai is Emeritus Professor of Mathematics and Statistics at McGill
University, Canada, and Director of the Centre for Mathematical and Statistical
Sciences, India. He has published over 300 research papers and more than 25
books on topics in mathematics, statistics, physics, astrophysics, chemistry,
and biology. He is a Fellow of the Institute of Mathematical Statistics,
National Academy of Sciences of India, President of the Mathematical Society of
India, and a Member of the International Statistical Institute. He is the
founder of the Canadian Journal of Statistics and the Statistical Society of
Canada. He is instrumental in the implementation of the United Nations Basic
Space Science Initiative. The paper is an attempt to capture the broad spectrum
of scientific endeavors of Professor A.M. Mathai at the occasion of his
anniversary.Comment: 21 pages, LaTe
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