Average equidistribution and statistical independence properties of digital inversive pseudorandom numbers over parts of the period

Emmerich, Frank

doi:10.1090/S0025-5718-01-01328-X

Average equidistribution and statistical independence properties of digital inversive pseudorandom numbers over parts of the period
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by Frank Emmerich;

Math. Comp. 71 (2002), 781-791

DOI: https://doi.org/10.1090/S0025-5718-01-01328-X

Published electronically: October 25, 2001

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Abstract:

This article deals with the digital inversive method for generating uniform pseudorandom numbers. Equidistribution and statistical independence properties of the generated pseudorandom number sequences over parts of the period are studied based on the distribution of tuples of successive terms in the sequence. The main result is an upper bound for the average value of the star discrepancy of the corresponding point sets. Additionally, lower bounds for the star discrepancy are established. The method of proof relies on bounds for exponential sums.

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