Quotation Derflinger, Gerhard, Hörmann, Wolfgang, Leydold, Josef. 2010. Random Variate Generation by Numerical Inversion when only the Density Is Known. ACM Transactions on Modeling and Computer Simulation 20 (4): 18:1-18:25.




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.


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Publication's profile

Status of publication Published
Affiliation WU
Type of publication Journal article
Journal ACM Transactions on Modelling and Computer Simulation
Citation Index SCI
WU-Journal-Rating new WH-B
Language English
Title Random Variate Generation by Numerical Inversion when only the Density Is Known
Volume 20
Number 4
Year 2010
Page from 18:1
Page to 18:25
Reviewed? Y
URL http://doi.acm.org/10.1145/1842722.1842723


Derflinger, Gerhard (Former researcher)
Leydold, Josef (Details)
Hörmann, Wolfgang (Turkey)
Institute for Statistics and Mathematics IN (Details)
Research Institute for Computational Methods FI (Details)
Research areas (ÖSTAT Classification 'Statistik Austria')
1114 Numerical mathematics (Details)
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