Several extensively tested multiple recursive random number generators

Several extensively tested multiple recursive random number generators

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Article ID: iaor19991506
Country: United Kingdom
Volume: 36
Issue: 6
Start Page Number: 129
End Page Number: 136
Publication Date: Sep 1998
Journal: Computers & Mathematics with Applications
Authors: ,
Keywords: probability
Abstract:

The Multiple Recursive Generator (MRG) has been considered by many scholars as a very good Random Number (RN) generator. This paper applies a sequential search to identify the MRGs of orders one, two, and three which are able to produce RNs with good lattice structure in terms of the spectral value and Beyer quotient. To detect departures from local randomness and homogeneity, extensive statistical tests including runs, auto-correlation, chi-square, serial, and the sparse occupancy tests have been conducted. In approximately 19.3 billion candidates, only four MRGs, namely, (1280550, –45991), (0, 45991, 1758790), (885300443, 0, 1552858447), and (885300443, 1546795921, 598295599), have passed all the theoretical and empirical tests. Among these (0, 45991, 1758790) can be implemented efficiently by applying the approximate factoring method and is therefore most recommended.

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