Bicriterial method for constructing and evaluating the quality of the histograms

In this article we propose a new method of constructing a histogram based on the evaluation of their quality bicriterial. One of the evaluation criteria is the reliability of a segment a histogram, and the second one is the consistency of the empirical distribution function and the distribution function, constructed from the histogram. The value of the first criterion increases with decreasing the number of half-open interval histograms, while the value of the second criterion increases with the number of half-open interval. Comprehensive quality criterion histogram which we introduced in the article allows for the first time to assess the quality of the histogram. Maximizing the value of the proposed criterion leads to the determination of the optimal number of segments of the histogram, which improves the reliability of the decisions of the received based on the sample, in particular, the approximation of the observed random variable to some well-known law of distribution.