A combinatorial method of small sample identification

Abstract

Aim. For the purpose of improving the reliability of decisions regarding the uniformity of distributions over samples of limited size, a combinatorial method has been developed for defining a criterion based on simple combinations of sample values. Methods. The paper uses methods of the probability theory, mathematical statistics, and combinatorics. Results. The proposed criterion is highly efficient for distinguishing small samples when testing statistically similar hypotheses, such as the hypothesis of a uniform distribution law and the hypothesis of a beta distribution of the first kind. Conclusions. The approach proposed in the paper enables a sequential analysis procedure (detection of process “imbalance”). This procedure makes it possible to reliably detect the “imbalance” (deviation of the distribution of observations from the uniform law) of a process with a practically sufficient intensity using recurrent relations.