Realization of Statistical Models Based on Symmetric Unimodal Distributions

The growing complexity of modern technical systems and increasing demands for operational efficiency necessitate more advanced numerical models and methods. This article addresses the development and analysis of statistical models, emphasizing a generalizing approach that derives the integral distribution function by reducing the degree of sub-integral expressions. The residual part is treated as modeling error, allowing pseudorandom value generation algorithms with accuracy limited only by computational power. A method is proposed for generating pseudorandom numbers through the sum of pseudorandom values, solving the problem of constructing a symmetric unimodal distribution with desired probabilistic properties. This is achieved via pairwise weighted summation of elements from standard sequences. Key analytical expressions underlying the method are derived and presented. Comprehensive computational experiments inform several improvements: enhanced decision-making in estimating probabilistic characteristics using symmetric unimodal distribution families; refined determination of confidence interval boundaries that reflect the accuracy of pseudorandom sequence reproduction in the Mathcad۱۵ environment; improved procedures for forming and evaluating basic sequences of pseudorandom variables, leading to better generation precision.

کلیدواژه ها:

symmetric unimodal distribution ، Skewness ، kurtosis index ، sample ، Random variable