The method of specification the degree of reliability for “zero hypotheses” about the distribution laws basing on Pearson's and Kolmogorov's consent criteria

In the recent years the modern socio-economic indicators usually are very unstable. Therefore the using of initial (raw) data even in the so-called “small samples” volume (25–30 values) could be problematic [1]–[3]. For the initial data now it is often necessary to use the small number of cases and observations i.e. the ultra-small samples which add some technical restrictions when we arestudying many problems in the mathematical statistics framework, in particular when analyzing the task of the Pearson's consent criteria
$\chi^{2}$
calculating with the recommended significance level
$\mathbf{R}_{\mathbf{predet. }}{\geq 95 \%}$
(i.e. “predetermined level”). In this research we propose the method of “(re)conciliation” (or “concordance”) for the determining and calculating the type of distribution laws for the random variable when
$\mathbf{R}_{\mathbf{calc. }}<\mathbf{R}_{\mathbf{predet. }}$
(i.e.
$\mathbf{R}_{\mathbf{calculated }}<\mathbf{R}_{\mathbf{predetermined }})$
. After that we created the “discrepancy criterion” (or “non-conformity criterion”) for the “zero hypotheses” concerned with the distribution laws of random variables testing for ultra-small samples cases.