Key Takeaway: This paper presents a complex generator for pseudo-random number generation, revealing that at least 950 homogeneous linear congruential generators with the smallest multiplier are needed to produce a usable stochastic uniform distribution.

Abstract

The present paper brings further elaboration of the methods introduced in [6] for evaluation of pseudo-random number generators. A very complex generator is constructed that can serve as canon for simulation of the true natural stochastic uniform distribution. Also, by extensive use of Monte Carlo method more precise and more complete data on the involved parameters are obtained. These data are then applied in an attempt to obtain some intuitive insight regarding certain principle that may become crucial point in founding statistical arithmetic. The main result should read: at least 950 homogeneous linear congruential generators with the smallest multiplier (i.e., 2) are needed in order that a permuting and shuffling algorithm produces a usable stochastic uniform distribution C/[0,l). The introduced canonical generator is also used to develop a more precise stochastic evaluation of PRN generators. This is accomplished by generation of large number of large samples so that approximation by normal distribution yields sufficiently close intervals of confidence.