Estimation of traditional numerical characteristics of lognormal distribution laws of a one-dimensional random variable in conditions of large volume statistical data

Abstract

The efficiency of estimating the numerical characteristics of a family of the lognormal distribution law of a onedimensional random variable under conditions of large volumes of statistical data is considered. To circumvent the problem of large samples, methods of discretization the range of values of a random variable based on the formulas of Sturges, Brooks-Carruthers, Heinhold-Gaede and the formula proposed by the authors of this article are used. Data arrays have been generated that make it possible to evaluate the numerical characteristics of the laws of distribution of random variables, taking into account their discrete values. Based on the transformed data arrays, estimates of the mathematical expectation, standard deviation, skewness and kurtosis coefficients were calculated. Estimates of the numerical characteristics of the considered distribution laws under the conditions of a continuous and discrete random variable are compared for different volumes of initial statistical data. The effectiveness of methods for estimating the numerical characteristics of the family of the lognormal distribution law based on the initial statistical data and on the results of transformations of these data using known discretization formulas has been established. The reliability of the comparison of the effectiveness indicators of the studied methods was confirmed by using the Kolmogorov-Smirnov criterion. It is shown that the discretization formula proposed by the authors of this article is better and more effective compared to traditional methods.