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On the Average Discrepancy of Successive Tuples of Pseudo-Random Numbers over Parts of the Period

Abstract.

 In the present paper we give an upper and a lower bound for the average value of the discrepancy of non-overlapping s-tuples of successive elements of a first order congruential pseudo-random-number generator (with prime modulus and maximal period). The estimates are – up to logarithmic factors – sharp also for short parts of the period.

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Received 30 January 1997; in revised form 2 May 1997

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Larcher, G., Wolf, R. & Eichenauer‐Herrmann, J. On the Average Discrepancy of Successive Tuples of Pseudo-Random Numbers over Parts of the Period. Mh Math 127, 141–154 (1999). https://doi.org/10.1007/s006050050029

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  • DOI: https://doi.org/10.1007/s006050050029

  • 1991 Mathematics Subject Classification: 11K45
  • Key words: Pseudo-Random numbers
  • discrepancy
  • serial test