Non-parametric statistics of random variables with unknown probability distribution functions

Abstract

The paper is devoted to the actual problem of data analysis with unknown distributions, where classical parametric methods are ineffective. On the example of two types of distribu-tions (logistic (symmetric) and exponential (asymmetric)), the application of a nonparametric approach, which consists of the stages of ranking and analysis of extreme values, is shown. Purpose: to conduct a qualitative analysis of the statistical homogeneity of time series by evaluating the main special criteria of samples - shifts and scales, to identify the advantages of such approaches for determining or further verifying the statistical homogeneity of time series samples. Research methods: The paper uses basic methods of nonparametric statistics: nonparametric criteria for statistical homogeneity are applied to simulation models of sam-ples. For samples with logistic and exponential distribution laws, their statistical parameters were found and analyzed and tested for statistical homogeneity. Practical novelty of the study: the approach to testing for statistical homogeneity presented in the paper expands the practical scope of applying nonparametric statistics methods for complex statistical analysis of time series with a distribution law other than normal. Applications: the results of the study can be used in areas requiring the analysis of statistical homogeneity of data, in particular in engineering to monitor the condition of technical objects and systems, in sociological re-search to identify significant differences between groups, in the medical field to control the quality of laboratory measurements.