## Retrospective Theses and Dissertations

Dissertation

1981

#### Degree Name

Doctor of Philosophy

Statistics

#### Abstract

In any successful simulation studies, pseudorandom number generators play the central roles, in terms of either efficiency or accuracy. The pseudorandom number generators under investigation here are the normal, noncentral, multinomial, hypergeometric and finally, a congruential uniform random number generator with arbitrary period lengths;The newly devised algorithm R-T-T for the normal distribution shows great promise in both accuracy and efficiency. The R-T-T algorithm combines the method of mixtures with the Alias algorithm, resulting in a generation time close to that of the uniform random variates generation;Since most of the noncentral distributions such as noncentral F, noncentral beta, noncentral t, etc., relate simply to noncentral chisquare distribution, the investigation is then focused on the latter. The other noncentrally distributed random variates can be obtained through simple transformations. Four algorithms are suggested here, two of which are moment approximations to the central chisquare distribution, the others being a normal approximation and an exact algorithm;The class of random multivariates under study here is the multinomial. A decomposition method of the multinomials into binomials in combination with an exact random median method is employed to yield a very efficient generator;The hypergeometric distribution can be considered as a binomial distribution in sampling without replacement after each Bernoulli trial. There is no closed form inverse transformation for this distribution. Two algorithms are devised here to increase the efficiency in generation. The first is based on a rejection method with the majoring function being an adjusted binomial and the second combines the Alias algorithm and the recurrence relationship of the probability densities of the distribution;Finally, a congruential uniform random number generator with arbitrary period lengths is introduced which utilizes extended arithmetic approach. The new generator can be used in any computer environments and to duplicate exact sequences generated by other congruential uniform random number generators of different period lengths.

#### DOI

https://doi.org/10.31274/rtd-180813-4680

#### Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/

#### Copyright Owner

Fred Chung-Man Ho

en

AAI8128828

application/pdf

137 pages

COinS