Equivalent Models of Random Data Distribution Functions

Abstract

This paper presents the results of the research carried out by the authors in the process of forming the report "Equivalence of random data distribution densities", delivered at the International Scientific and Practical Conference "Information Technologies and Computer Modeling (ITСM-24)", held in Ivano-Frankivsk in the period from May 21 to 24, 2024, in which the method for the synthesis of a statistical estimate of the equivalent density of a random data distribution is proposed, which does not require "histogram alignment" using the Pearson -distribution. At the first stage, the method proposed by the authors uses the crunching of a histogram constructed using a relatively small sample of random data, followed by cumulative summation to determine the equivalent distribution function of these data on a set of their available values. At the second stage of the method proposed by the authors, the constructed equivalent distribution function of random data is interpolated by cubic splines according to the algorithm that uses the mathematical relations derived by the authors. And at the third stage of the method proposed by the authors, by differentiating the equivalent mathematical model of the distribution of random data, obtained at the previous stages of the implementation of this method, an equivalent mathematical model of the density of the distribution of random data is synthesized, using which the primary base histogram was created. The paper contains or mentions all the Python programs necessary for the implementation of all stages of the proposed method of synthesis of the equivalent density model of the random data distribution , as well as the example of solving a specific practical problem with explanations of all actions necessary to perform at each of the stages implementation of the proposed method.