The Complete Set Simulation of Stochastic Sequences without Repeated and Skipped Elements

Aleksei F. Deon (N.E. Bauman Moscow State Technical University, Russia)

Yulian A. Menyaev (University of Arkansas for Medical Sciences, USA)

Abstract: Random sequences are widely used in theoretical and practical areas of interests in human and technical activities. An important part of these fields is referred to as the procedures of producing stochastic values. One direction adapts the sequenced generating of pseudorandom numbers and the other direction uses all stochastic sequences in objects of completed sets. The first direction is well studied and is traditionally used in cryptography and technical systems in medical and biological trials. The second direction is generally used in systems for preliminary universal testing where all or characteristically important sequences belong to a given diapason of actions are required. In this current work we explore the second direction, where the underlying approaches in modern generators of random numbers are considered. The simulation of complete sets of random numbers shows that either skipping or repeating of generated values is possible. We've formed the requirements that if followed, the problems of skipping and repeating are overcome. Next, we’ve proposed novel algorithms to form completed ranked sets of random sequences. Also, we've proposed novel algorithms on the basis of factorial expansion of random numbers which provide fast generation of such sequences. A discussion of the advantages and disadvantages of the indicated statements completes this paper.

Keywords: computer simulation, probability and statistics, random number generator, stochastic sequence algorithm

Categories: F.2, G.2.1, G.3