A guide to simulation (2nd ed.)
A guide to simulation (2nd ed.)
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Accurate monotone cubic interpolation
SIAM Journal on Numerical Analysis
A rejection technique for sampling from T-concave distributions
ACM Transactions on Mathematical Software (TOMS)
C1 comonotone Hermite interpolation via parametric cubics
Journal of Computational and Applied Mathematics
Automatic sampling with the ratio-of-uniforms method
ACM Transactions on Mathematical Software (TOMS)
Simulation Modeling and Analysis
Simulation Modeling and Analysis
Monotonic generation of positive random variables
WSC '83 Proceedings of the 15th conference on Winter simulation - Volume 1
A Gaussian Noise Generator for Hardware-Based Simulations
IEEE Transactions on Computers
A Hardware Gaussian Noise Generator Using the Box-Muller Method and Its Error Analysis
IEEE Transactions on Computers
Black-box algorithms for sampling from continuous distributions
Proceedings of the 38th conference on Winter simulation
A compact and accurate Gaussian variate generator
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Generating inverse Gaussian random variates by approximation
Computational Statistics & Data Analysis
Random variate generation by numerical inversion when only the density is known
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Generating generalized inverse Gaussian random variates by fast inversion
Computational Statistics & Data Analysis
Quasi-Monte Carlo Method for Infinitely Divisible Random Vectors via Series Representations
SIAM Journal on Scientific Computing
A hardware gaussian noise generator using the wallace method
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Simulating Lévy Processes from Their Characteristic Functions and Financial Applications
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Inverse transform method for simulating Levy processes and discrete Asian options pricing
Proceedings of the Winter Simulation Conference
Numerical inverse Lévy measure method for infinite shot noise series representation
Journal of Computational and Applied Mathematics
A Monte Carlo algorithm for degenerate plasmas
Journal of Computational Physics
RENETO, a realistic network traffic generator for OMNeT++/INET
Proceedings of the 6th International ICST Conference on Simulation Tools and Techniques
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The inversion method for generating nonuniform random variates has some advantages compared to other generation methods, since it monotonically transforms uniform random numbers into non-uniform random variates. Hence, it is the method of choice in the simulation literature. However, except for some simple cases where the inverse of the cumulative distribution function is a simple function we need numerical methods. Often inversion by "brute force" is used, applying either very slow iterative methods or linear interpolation of the CDF and huge tables. But then the user has to accept unnecessarily large errors or excessive memory requirements, that slow down the algorithm. In this article, we demonstrate that with Hermite interpolation of the inverse CDF we can obtain very small error bounds close to machine precision. Using our adaptive interval splitting method, this accuracy is reached with moderately sized tables that allow for a fast and simple generation procedure.