Random Number Generation and its Better Technique

Abstract

Random number generators based on linear recurrences modulo 2 are among the fastest long-period generators currently available. The uniformity and independence of the points they produce, over their entire period length, can be measured by theoretical figures of merit that are easy to compute, and those having good values for these figures of merit are statistically reliable in general. Some of these generators can also provide disjoint streams and substreams efficiently. In this paper, we review the most interesting construction methods for these generators, examine their theoretical and empirical properties, and make comparisons. Random number generation is the art and science of deterministically generating a sequence of numbers that is difficult to distinguish from a true random sequence. This thesis introduces the field of random number generation, and studies three types of random number generators in depth. It also includes mathematical techniques for transforming the output of generators to arbitrary distributions, and methods of evaluating and comparing random number generators. It concludes with a summary and historical perspective on the field of random number generation. The mathematics in this thesis is drawn mainly from number theory, with a few fundamental ideas taken from probability and statistics.