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On Exact Sampling of Nonnegative Infinitely Divisible Random Variables

Part of: Stochastic processes Distribution theory - Probability

Published online by Cambridge University Press:  04 January 2016

Zhiyi Chi
Zhiyi Chi*
Affiliation:
University of Connecticut
*
∗ Postal address: Department of Statistics, University of Connecticut, 215 Glenbrook Road, U-4120, Storrs, CT 06269, USA. Email address: zhiyi.chi@uconn.edu
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Abstract

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Nonnegative infinitely divisible (i.d.) random variables form an important class of random variables. However, when this type of random variable is specified via Lévy densities that have infinite integrals on (0, ∞), except for some special cases, exact sampling is unknown. We present a method that can sample a rather wide range of such i.d. random variables. A basic result is that, for any nonnegative i.d. random variable X with its Lévy density explicitly specified, if its distribution conditional on X ≤ r can be sampled exactly, where r > 0 is any fixed number, then X can be sampled exactly using rejection sampling, without knowing the explicit expression of the density of X. We show that variations of the result can be used to sample various nonnegative i.d. random variables.

Keywords

Infinitely divisiblerejection samplingexact samplingsubordinatorLévy process

MSC classification

Primary: 60E07: Infinitely divisible distributions; stable distributions
Secondary: 60G50: Sums of independent random variables; random walks
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 44 , Issue 3 , September 2012 , pp. 842 - 873
Copyright
© Applied Probability Trust 

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