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

The efficiency of estimating the traditional numerical characteristics of multimodal symmetric and asymmetric distribution laws of a one-dimensional random variable with large amounts of statistical data is considered. To circumvent the problem of large samples, the formulas for discretization of the interval of values of a random variable by Sturgess, Brooks-Carruthers, Heinhold-Gaede and the formula for optimal discretization proposed by the authors of this article were used. For this purpose, data arrays have been formed that allow us to evaluate the numerical characteristics of the laws of distribution of random variables, taking into account their discrete values. Estimates of mathematical expectation, mean square deviation, coefficients of asymmetry and kurtosis are calculated from the transformed data sets. Estimates of the numerical characteristics of the considered distribution laws for continuous and discrete random variables with different volumes of initial statistical data are compared. The efficiency of methods for estimating the numerical characteristics of multimodal distribution laws based on initial statistical information and the results of transforming this information using the specifi ed discretization formulas has been established. The reliability of comparing the performance indicators of the studied methods was confirmed using the Kolmogorov-Smirnov criterion. It is shown that the Heinhold-Gaede formula and the optimal discretization formula proposed by the authors are more effective than the Sturgess and Brooks-Carruthers discretization formulas. The obtained results can be used in processing remote sensing data of natural objects, which are characterized by a large volume of statistical information and multimodal laws of distribution of spectral features.