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

The efficiency of estimating the numerical characteristics of the family of the lognormal law of distribution of a one-dimensional random variable with large amounts of statistical data is considered. To circumvent the problem of large samples, methods for discretizing the range of values of a random variable based on the Sturgess, Brooks-Carruther, Heinhold-Gaede formulas and the formula proposed by the authors of this article are used. Data arrays have been formed that make it possible to estimate the numerical characteristics of the distribution laws of random variables, taking into account their discrete values. Based on the transformed data sets, estimates of mathematical expectation, standard deviation, asymmetry and kurtosis coefficients were calculated. Estimates of the numerical characteristics of the considered distribution laws for a continuous and discrete random variable with different volumes of initial statistical data are compared. The effectiveness of methods for estimating the numerical characteristics of the family of the lognormal distribution law from the initial statistical data and from 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 using the Kolmogorov-Smirnov criterion. It is shown that the discretization formula proposed by the authors of this article is more efficient in comparison with the traditional Sturgess, Brooks-Carruther, and Heinhold-Gaede discretization formulas.