Issues of identification of the distribution of sampled data with the limitation of the lower boundary of scattering of the observed values

Abstract

Statistical analysis of empirical data is a commonly used approach for research in various fields of science and in applications, including studies of economic processes and critical conditions, but at the same time, there are numerous questions regarding the selection of theoretical distribution laws in general populations that include the sample data being studied. This selection is required for reliable forecasting of risks and reliability because these tasks require the prediction of rather small probabilities or, conversely, the probabilities that approach 1.0. For studying issues with numerical identification of empirical data, a software tool has been developed; it includes drawing of pseudo-random samples from Weibull distribution with a given lower threshold of dispersion, followed by the determination of whether the samples belong to the original distribution or to the normal distribution. A numerical experiment has been carried out with a wide range of variation in the parameters of the considered distributions and using the Pearson's goodness-of-fit test for identification of the sample datas distribution. An analysis of the results of the numerical modeling, which incorporated significant variation of the volume of the samples and their parameters, showed the high probability of false identification of the normal distribution of the sample data, whereas, in fact, the samples were drawn from Weibull distribution with a fixed lower threshold of dispersion.