Генерація псевдовипадкових чисел на основі рекурентних співвідношень і їх статистичний аналіз

Abstract

This paper addresses the problem of software implementation and verification of pseudo-random number generators based on recurrence relations. The object of the study is the Linear Congruential Generator (LCG), implemented using the C++ programming language. During the work, software was developed to generate numerical sequences utilizing a timestamp to ensure sample uniqueness. A comprehensive statistical analysis of the obtained data was conducted, including the calculation of the expected value, variance, and standard deviation. To test the hypothesis of a uniform distribution, a frequency analysis method with histogram construction was applied. The experimental results confirm the effectiveness of the applied algorithm and the compliance of the generated numbers with statistical quality criteria.