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An empirical study of locally pseudo-random sequences Dobell, Alan Rodney

Abstract

In Monte Carlo calculations performed on electronic computers it is advantageous to use an arithmetic scheme to generate sets of numbers with "approximately" the properties of a random sequence. For many applications the local characteristics of the resulting sequence are of interest. In this thesis the concept of a pseudo-random sequence is set out, and arithmetic methods for their generation are discussed. A brief survey of some standard statistical tests of randomness is offered, and the results of empirical tests for local randomness performed on the ALWAC III-E computer at the University of British Columbia are recorded. It is demonstrated that many of the standard generating schemes do not yield sequences with suitable local properties, and could therefore be responsible for misleading results in some applications. A method appropriate for the generation of short blocks of numbers with approximately the properties of a randomly selected set is proposed and tested, with satisfactory results.

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