TWO-COMPONENT INDEPENDENCE EXPRESS TESTING METHOD FOR SEQUENCES OF PSEUDO-RANDOM NUMBERS

Abstract

Random and pseudo-random number generators are involved in solving a significant number of problems through simulation modeling. The sufficient randomness or unpredictability is essential for sequences of random numbers (RNSs). This paradigm of sufficient randomness is the basis for many test systems available now. We suggest that it is more appropriate to understand random variables in the tasks of random processes simulation as models of probability theory, where all properties of variables are determined by their distribution functions. A complete analysis of the RNSs pairs statistical independence must be carried out through defining the necessary and sufficient conditions: the joint probabilities are equal to the products of the corresponding marginal probabilities. This approach leads to the need of solving problems in a two-dimensional space with the NxN order of algorithms, where N is the length of the RNSs.

This work proposes a two-component test, that includes: a) testing the correspondence of the RNSs sums distribution function to the theoretical distribution function of independent random variables sums; b) a non-correlation test. The joint application of this tests pair allows to distinguish between dependent and independent RNSs with sufficient degree of certainty. In this case, the order of algorithms is only N, since the problems are solved in a one-dimensional space. Thus, the proposed approach allows to solve problems involving extremely large arrays of random numbers, i.e. the Big Data problems.

The proposed method of two-component testing is validated on samples of pseudo-random numbers generators of the NumPy library for the Python programming language. For the uniformly and normally distributed RNSs, the proposed method showed compliance with theoretical estimates of the wrong decisions probability, as well as a sufficiently high speed of data processing, which allows to recommend it be used in express tests of RNSs.