TY - UNPB

T1 - Online Supplement to "Random Variate Generation by Numerical Inversion When Only the Density Is Known"

AU - Derflinger, Gerhard

AU - Hörmann, Wolfgang

AU - Leydold, Josef

PY - 2009/9/1

Y1 - 2009/9/1

N2 - This Online Supplement summarizes our computational experiences with Algorithm NINIGL presented in our paper "Random Variate Generation by Numerical Inversion when only the Density Is Known" (Report No. 90). It is 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 these 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. Thus our algorithm is especially attractive for the simulation of copulas and for quasi-Monte Carlo applications.

AB - This Online Supplement summarizes our computational experiences with Algorithm NINIGL presented in our paper "Random Variate Generation by Numerical Inversion when only the Density Is Known" (Report No. 90). It is 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 these 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. Thus our algorithm is especially attractive for the simulation of copulas and for quasi-Monte Carlo applications.

M3 - WU Working Paper

T3 - Research Report Series / Department of Statistics and Mathematics

BT - Online Supplement to "Random Variate Generation by Numerical Inversion When Only the Density Is Known"

ER -