An automatic method for generating random variates with a given characteristic function
SIAM Journal on Applied Mathematics
SIAM Journal on Scientific and Statistical Computing
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Precise tabulation of the maximally-skewed stable distributions and densities
Computational Statistics & Data Analysis
Generating gamma variates by a modified rejection technique
Communications of the ACM
Numerical methods of statistics
Numerical methods of statistics
An Introduction to Copulas (Springer Series in Statistics)
An Introduction to Copulas (Springer Series in Statistics)
Evaluation of Tweedie exponential dispersion model densities by Fourier inversion
Statistics and Computing
Computational Statistics & Data Analysis
Numerical Methods for Laplace Transform Inversion
Numerical Methods for Laplace Transform Inversion
Sampling Exponentially Tilted Stable Distributions
ACM Transactions on Modeling and Computer Simulation (TOMACS)
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This paper discusses simulation from an absolutely continuous distribution on the positive real line when the Laplace transform of the distribution is known but its density and distribution functions may not be available. We advocate simulation by the inversion method using a modified Newton-Raphson method, with values of the distribution and density functions obtained by numerical transform inversion. We show that this algorithm performs well in a series of increasingly complex examples. Caution is needed in some situations when the numerical Laplace transform inversion becomes unreliable. In particular the algorithm should not be used for distributions with finite range. But otherwise, except for rather pathological distributions, the approach offers a rapid way of generating random samples with minimal user effort. We contrast our approach with an alternative algorithm due to Devroye (Comput. Math. Appl. 7, 547---552, 1981).