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Random Variate Generation by Numerical Inversion When Only the Density Is Known

Derflinger, Gerhard and Hörmann, Wolfgang and Leydold, Josef (2009) Random Variate Generation by Numerical Inversion When Only the Density Is Known. Research Report Series / Department of Statistics and Mathematics, 90. Department of Statistics and Mathematics, WU Vienna University of Economics and Business, Vienna.

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Abstract

We present a numerical inversion method for generating random variates from continuous distributions when only the density function is given. The algorithm is based on polynomial interpolation of the inverse CDF and Gauss-Lobatto integration. The user can select the required precision which may be close to machine precision for smooth, bounded densities; the necessary tables have moderate size. Our computational experiments with the classical standard distributions (normal, beta, gamma, t-distributions) and with the noncentral chi-square, hyperbolic, generalized hyperbolic and stable distributions showed that our algorithm always reaches the required precision. The setup time is moderate and the marginal execution time is very fast and nearly the same for all distributions. Thus for the case that large samples with fixed parameters are required the proposed algorithm is the fastest inversion method known. Speed-up factors up to 1000 are obtained when compared to inversion algorithms developed for the specific distributions. This makes our algorithm especially attractive for the simulation of copulas and for quasi-Monte Carlo applications. <P> This paper is the revised final version of the working paper no. 78 of this research report series.

Item Type: Paper
Additional Information: Paper published in ACM Transactions on Modeling and Computer Simulation. (c) ACM (2009). This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in ACM Trans. Model. Comput. Simul. Vol. 20, No. 4 (2010) DOI: http://doi.acm.org/10.1145/1842722.1842723.
Keywords: non-uniform random variates / inversion method / universal method / black-box algorithm / Newton interpolation / Gauss-Lobatto integration
Classification Codes: CCS G.3
Divisions: Departments > Finance, Accounting and Statistics > Statistics and Mathematics
Depositing User: Repository Administrator
Date Deposited: 16 Sep 2009 14:38
Last Modified: 20 Sep 2017 04:34
URI: http://epub.wu.ac.at/id/eprint/162

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