Variational criterion of evenness

Abstract

Abstract. Aim. The author has developed a criterion to test the hypothesis of a uniform distribution for random variable observations in small samples. The criterion is built by using sample observations to construct a variation series in ascending order and dividing each previous term of this series by the extreme term, then discarding it. The resulting new variation series is processed similarly until there is only one quotient left that is the criterion value.

Methods. The paper uses methods of the probability theory and mathematical statistics.

Results. The suggested criterion is sufficiently efficient for distinguishing between samples of minimal size for 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 suggested in the paper makes it quite simple to implement the sequential analysisprocedure (detection of a “dissonance” in a process). Such a procedure allows detecting a “dissonance” (deviation of the distribution of observations from the uniform law) with a practically sufficient rate.