Thesis (M. Phil.)--University of Hong Kong, 2009. / Includes bibliographical references (leaves 61-66) Also available in print.

by Lee Kim-hung. / Thesis (M.Phil.)--Chinese University of Hong Kong. / Bibliography: leaf 60.

Project (M.S.)--Brigham Young University. Dept. of Statistics, 2005. / Includes bibliographical references (p. 82-85).

Thesis (Ph. D.)--Western Michigan University, 2001. / Also available on the World Wide Web at above URL. Includes bibliographical references (leaves 94-102).

Thesis (M.S.)--George Mason University, 2009. / Vita: p. 91. Thesis director: Jens-Peter Kaps. Submitted in partial fulfillment of the requirements for the degree of Master of Science in Computer Engineering. Title from PDF t.p. (viewed Oct. 12, 2009). Includes bibliographical references (p. 88-90). Also issued in print.

Thesis (M.C.S.)--Carleton University, 1992. / Also available in electronic format on the Internet.

published_or_final_version / Computer Science / Master / Master of Philosophy

Random number generators (RNGs) are widely used in conducting Monte Carlo simulation studies, which are important in the field of statistics for comparing power, mean differences, or distribution shapes between statistical approaches. Statistical results, however, may differ when different random number generators are used. Often older methods have been blindly used with no understanding of their limitations. Many random functions supplied with computers today have been found to be comparatively unsatisfactory. In this study, five multiplicative linear congruential generators (MLCGs) were chosen which are provided in the following statistical packages: RANDU (IBM), RNUN (IMSL), RANUNI (SAS), UNIFORM(SPSS), and RANDOM (BMDP). Using a personal computer (PC), an empirical investigation was performed using five criteria: period length before repeating random numbers, distribution shape, correlation between adjacent numbers, density of distributions and normal approach of random number generator (RNG) in a normal function. All RNG FORTRAN programs were rewritten into Pascal which is more efficient language for the PC. Sets of random numbers were generated using different starting values. A good RNG should have the following properties: a long enough period; a well-structured pattern in distribution; independence between random number sequences; random and uniform distribution; and a good normal approach in the normal distribution. Findings in this study suggested that the above five criteria need to be examined when conducting a simulation study with large enough sample sizes and various starting values because the RNG selected can affect the statistical results. Furthermore, a study for purposes of indicating reproducibility and validity should indicate the source of the RNG, the type of RNG used, evaluation results of the RNG, and any pertinent information related to the computer used in the study. Recommendations for future research are suggested in the area of other RNGs and methods not used in this study, such as additive, combined, mixed and shifted RNGs.

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