# Computer Generation of Random Variables Using the Ratio of Uniform Deviates

@article{Kinderman1977ComputerGO, title={Computer Generation of Random Variables Using the Ratio of Uniform Deviates}, author={Albert J. Kinderman and John F. Monahan}, journal={ACM Trans. Math. Softw.}, year={1977}, volume={3}, pages={257-260} }

The ratio-of-uniforms method for generating random variables having continuous nonuniform distributions is presented. In thin method a point is generated uniformly over a particular region of the plane. The ratio of the coordinate values of thin point yields a deviate with the desired distribution. Algorithms which utilize this techmque are generally short and often as fast as longer algorithms.

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## 212 Citations

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### Efficient generation of random variates via the ratio-of-uniforms method

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Improvements to the conventional ratio-of-uniforms method for random variate generation are proposed. A generalized radio-of-uniforms method is introduced, and it is demonstrated that relocation of…

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Lower bounds for probabilities only depending on the modulus and the Beyer quotient of the LCG are proved for the case that Cauchy normal or exponential random numbers are generated, justifying the recommendation not to use the ratio of uniform method combined with LCGs.

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A random number generation method, which is one of the rejection methods, is presented, and to accelerate ratio-of-uniform method, an efficiency variabler is used.

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It is shown, that the ratio-of-uniforms method is also useful for the design of a black-box algorithm suitable for a large class of distributions, including all with log-concave densities.

### A fast normal random number generator

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A method is presented for generating pseudorandom numbers with a normal distribution using the ratio of uniform deviates method discovered by Kinderman and Monahan with an improved set of bounding curves and can be implemented in 15 lines of FORTRAN.

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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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An algorithm is presented for generating random variables from the chi family of distributions withdegrees of freedom parameter LY 2 1. It is based on the ratio of uniforms method and can be…

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### Received September

- Received September
- 1976