On monotone and convex spline interpolation
Mathematics of Computation
A method for computer generation of variates from arbitrary continuous distributions
SIAM Journal on Scientific and Statistical Computing
Numerical methods of statistics
Numerical methods of statistics
Numerical computing with IEEE floating point arithmetic
Numerical computing with IEEE floating point arithmetic
Continuous random variate generation by fast numerical inversion
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Approximations for Digital Computers
Approximations for Digital Computers
Gaussian random number generators
ACM Computing Surveys (CSUR)
Numerical Methods in Scientific Computing: Volume 1
Numerical Methods in Scientific Computing: Volume 1
Generating generalized inverse Gaussian random variates by fast inversion
Computational Statistics & Data Analysis
Original Articles: t-Copula generation for control variates
Mathematics and Computers in Simulation
New control variates for lévy process models
Proceedings of the Winter Simulation Conference
New control variates for Lévy process models
Proceedings of the Winter Simulation Conference
New control variates for Lévy process models
Proceedings of the Winter Simulation Conference
Numerical inverse Lévy measure method for infinite shot noise series representation
Journal of Computational and Applied Mathematics
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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.