Computer methods for sampling from gamma, beta, poisson and bionomial distributions

  title={Computer methods for sampling from gamma, beta, poisson and bionomial distributions},
  author={Joachim H. Ahrens and Ulrich Dieter},
Accurate computer methods are evaluated which transform uniformly distributed random numbers into quantities that follow gamma, beta, Poisson, binomial and negative-binomial distributions. All algorithms are designed for variable parameters. The known convenient methods are slow when the parameters are large. Therefore new procedures are introduced which can cope efficiently with parameters of all sizes. Some algorithms require sampling from the normal distribution as an intermediate step. In… 

Expected time analysis of a simple recursive Poisson random variate generator

  • L. Devroye
  • Mathematics, Computer Science
  • 2005
A well-known recursive method for generating Poisson random variables with parameter λ is considered, and it is shown how it can be manipulated to produce random variates at an expected time cost ofO(log log λ).

A simple algorithm for generating random variates with a log-concave density

  • L. Devroye
  • Mathematics, Computer Science
  • 2005
A short algorithm for generating random variates with log-concave density onR and known mode in average number of operations independent off and included in this class are the normal, gamma, Weibull, beta and exponential power, logistic, hyperbolic secant and extreme value distributions.

Sampling from binomial and poisson distributions: A method with bounded computation times

An accurate acceptance-rejection algorithm is devised and tested. The procedure requires an average of less than 3 uniform deviates whenever the standard deviation σ of the distribution is at least

Sampling from the poisson distribution on a computer

A method of sampling from the Poisson distribution on a computer that appears to be less costly than a recently suggested method in [1], and places an upper bound on the cost of generating a Poisson variate.

Generating beta variates via patchwork rejection

A new algorithm for sampling from beta(p, q) distributions with parametersp>1,q>1 is developed. It is based on a method by Minh [9] which improves acceptance-rejection sampling in the main part of

Initializing algorithms: A note to the article “Computer methods for sampling from gamma, beta, poisson and binomial distributions”

A general initialization principle is presented that increases the efficiency of algorithms in terms of computation time and results in significant performance improvements in the algorithm NS.

Computer methods for efficient sampling from largely arbitrary statistical distributions

A procedure is developed which prepares “guide tables” in order to facilitate this inversion so that sampling becomes efficient for arbitraryF(x), and the resulting sampling algorithm compares well with known general methods.

Closeness of Gamma and Generalized Exponential Distribution

Abstract Recently a new distribution, named as generalized exponential distribution or exponentiated exponential distribution was introduced and studied quite extensively by the authors. It is

Generating random numbers from a distribution specified by its Laplace transform

This paper advocates simulation by the inversion method using a modified Newton-Raphson method, with values of the distribution and density functions obtained by numerical transform inversion, and shows that this algorithm performs well in a series of increasingly complex examples.

Another special method to sample probability density functions

  • I. Lux
  • Mathematics, Computer Science
  • 2005
A modified rejection technique is proposed, to sample certain probability density functions, specific to reactor physical Monte Carlo calculations, and the efficiency of the new method is compared to that of the conventional rejection technique.



A combinatorial method for the generation of normally distributed random numbers

The proposed method generates standard normal variablesx using a variant of J. v. Neumann's algorithm for the generation of exponentially distributed random numbers and an acceptance-rejection approach of G. Marsaglia.

Pseudo-random numbers

The included ALGOL and FORTRAN subroutines will enable programmers to make practical use of this paper and indicate that the factors 4a ≈2k ξ are superior.

Von Neumann''s comparison method for random sampling from the normal and other distributions.

The author presents a generalization he worked out in 1950 of von Neumann''s method of generating random samples from the exponential distribution by comparisons of uniform random numbers on (0,1).

A Simple Algorithm for Generating Binomial Random Variables When N is Large

Abstract This article proposes a simple algorithm for generating binomial (N, p) random variables when N is large. The method involves looking mainly at medians in uniform (0, 1) samples of size

Extensions of Forsythe’s method for random sampling from the normal distribution

This article is an expansion of G. E. Forsythe's paper "Von Neumann's com- parison method for random sampling from the normal and other distributions" (5). It is shown that Forsythe's method for the

Pseudo-random numbers. The exact distribution of pairs

4bstract. Pseudo-random numbers are usually generated by linear congruential methods. Starting with an integer yo, a sequence (y1 j is constructed by yi+1 _ ay; + r (mod m), m, a, r being integers.

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.

An exact determination of serial correlations of pseudo-random numbers

SummaryExact expressions for serial correlations of sequences of pseudo-random numbers are derived. The reduction to generalized Dedekind sums is of optimum simplicity and covers all cases of the

A fast procedure for generating normal random variables

A technique for generating normally distributed random numbers is described. It is faster than those currently in general use and is readily applicable to both binary and decimal computers.