# Non-Uniform Random Variate Generation

@inproceedings{Devroye1986NonUniformRV, title={Non-Uniform Random Variate Generation}, author={Luc Devroye}, year={1986} }

This is a survey of the main methods in non-uniform random variate generation, and highlights recent research on the subject. Classical paradigms such as inversion, rejection, guide tables, and transformations are reviewed. We provide information on the expected time complexity of various algorithms, before addressing modern topics such as indirectly specified distributions, random processes, and Markov chain methods. Authors’ address: School of Computer Science, McGill University, 3480…

## 4,028 Citations

### Random Number and Variate Generation

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- 2013

This chapter discusses various methods for the generation of random samples distributed according to given probability distributions, in both the univariate and multivariate cases. These methods can…

### Uniform random number generation

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Practical ways of generating uniform variates for several classes of generators, such as linear congruential, multiple recursive, digital multistep, Tausworthe, lagged-Fibonacci, generalized feedback shift register, matrix, linear Congruential over fields of formal series, and combined generators are examined.

### The generation of binomial random variates

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The transformed rejection method, a combination of inversion and rejection, is well suited to generate binomial random variates as well and for the case that the parameters of the binomial distribution vary from call to call BTRD is faster than the current state of the art algorithms.

### Random-number and random-variate generation: automatic random variate generation for simulation input

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- 2000

Algorithms for generating random variates for simulation input based on the rejection principle, a mixture of naive resampling and sampling from the multi-normal distribution that has the same co-variance matrix as the data, and algorithms that generate random variate directly from a given sample by implicitly estimating the unknown distribution are presented.

### Random variate generation by numerical inversion when only the density is known

- Mathematics, Computer ScienceTOMC
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The proposed algorithm is based on polynomial interpolation of the inverse CDF and Gauss-Lobatto integration and is the fastest inversion method known for generating random variates from continuous distributions when only the density function is given.

### Density Estimation and Random Variate Generation

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- 2002

It is proved that the convergence to the true density for both the density estimation and random variate generation techniques at a rate where is the number of data points and can be made arbitrarily small for sufficiently smooth target densities, which is very close to the optimally achievable convergence rate under similar smoothness conditions.

### Automatic random variate generation for simulation input

- Computer Science2000 Winter Simulation Conference Proceedings (Cat. No.00CH37165)
- 2000

Algorithms for generating random variates for simulation input based on the rejection principle, a mixture of naive resampling and sampling from the multi-normal distribution that has the same covariance matrix as the data are developed and evaluated.

### THE TRANSFORMED REJECTION METHODFOR GENERATING RANDOM VARIABLES , AN ALTERNATIVE TO THE RATIO OF UNIFORMS

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Theoretical considerations and empirical results show that the one-dimensional quality of non-uniform random numbers is bad and the discrepancy is high when they are generated by the ratio of…

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