Equivalent Models of the Random Variable Distribution Laws

Abstract

It is substantiated that the determination of any characteristics of random variables can be reduced to computer calculations using the corresponding numerically determined integral laws of their distribution, and therefore the implementation of the stage of "equalization" of histograms with classical functions, which are proposed in classical mathematical statistics to approximate the random variable distribution laws, becomes unnecessary. A method of synthesis of equivalent models of the random variables distribution laws is proposed, in which instead of the procedure of "equalization" of histograms, a much simpler procedure of their approximation to numerically given integral distribution functions is implemented, which, after interpolation and differentiation, are transformed into equivalent models of differential laws of distribution in the event that the researcher has these laws for further studies are needed in a differential form. It is shown that the use of equivalent models of the random variable distribution laws when calculating their numerical characteristics gives results that are closer to the characteristics of the implementations of random variables generating these laws compared to the results that occur after the "equalization" of histograms by known classical functions using the Pirson procedure The effectiveness of the proposed method is demonstrated on the example of building a database suitable for identifying the laws of the distribution of grades of students who receive these grades while studying in a small-format group. The starting conditions for this example are taken from a specific previous publication of the authors, in which they created a database of student evaluations in a group of 10 people during their study: "Methodology and organization of scientific research in the field of information technologies."