MENTAL METHOD AND ITS PRACTICAL APPLICATIONS - Bakhtiyor Zokhirovich Usmonov; Eldor N. Xujayarov (Modern American Journals, 2025)
This article analyzes in detail the theoretical and practical foundations of the method of moments, which is widely used in statistical analysis and parameter estimation. The method of moments is of great importance in building statistical models, determining probability distribution parameters, and analyzing technical processes. With the help of this method, sample moments in a data set are equated to moments of the general population and unknown parameters are determined. The method of moments is distinguished by its simplicity in statistical calculations, convenience in mathematical analysis, and ease of use in various sciences. During the study, the advantages and disadvantages of the method of moments, as well as its real practical applications in the fields of economics, engineering, construction, mechanics, and physics, were shown through examples. This method provides fast and reliable results on large statistical data, but may lose some accuracy on small samples and extreme values. The method of moments is widely used today in many important areas, such as investment risk assessment, structural design, rotational dynamics analysis, and material resistance. The article emphasizes the need to develop the method of moments and further improve it through computer programs.
Keywords: Method of moments, statistical evaluation, structural analysis, physical modeling, parameter estimation, probability theory.