Computer Generation of Random Variables Using the Ratio of Uniform Deviates

  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.},
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. 

Tables from this paper

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

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

A note on the quality of random variates generated by the ratio of uniforms method

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.

Accuracy in random number generation

An ideal discrete approximation of a continuous distribution and a measure of error are proposed for the generation of continuous random variables on a digital computer and comments are made for the design of algorithms to reduce the bias and avoid overflow problems.

The generalized ratio-of-uniform method

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.

Computer generation of random variates from the tail of t and normal distributions

An algorithm is developed for the efficient generation of random variates from the tail of a t-distribution. This is specialised to the case of a Normal distribution. Theoretical measures of

Automatic sampling with the ratio-of-uniforms method

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

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.

The transformed rejection method for generating random variables, an alternative to the ratio of uniforms method

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

An algorithm for generating chi random variables

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



Algorithm 488: A Gaussian pseudo-random number generator

  • R. Brent
  • Mathematics, Computer Science
  • 1974
The algorithm calculates the exact cumulative distribution of the two-sided Kolmogorov-Smirnov statistic for samples with few observations for data sampling and discrete system simulation.

A Convenient Method for Generating Normal Variables

A normal random variable X may be generated in terms of uniform random variables $u_1 $, $u_2 $, in the following simple way: 86 percent of the time, put $X = 2(u_1 + u_2 + u_3 - 1.5)$,11 percent of

A Pseudo-Random Number Generator for the System/360

A particular pseudo-random number generator is described that uses the full 31-bit capacity of the registers in the IBM SYSTEM/360 computers and has been found to be highly satisfactory.

Computer methods for sampling from the exponential and normal distributions

The authors' primary conwiba~ion is the rise of polynomiaI sampling (as ex~ p/tiffed in Section 2) to eliminate any dependency on standard&ruction programs.

ACM Transactmns on Mathematical Software

  • ACM Transactmns on Mathematical Software
  • 1977

Received September

  • Received September
  • 1976