Application of the entropic coefficient for interval number optimization during interval assessment

Abstract

In solving many statistical problems, the most precise choice of the distribution law of a random variable is required, the sample of which the authors observe. This choice requires the construction of an interval series. Therefore, the problem arises of assigning an optimal number of intervals, and this study proposes a number of formulas for solving it. Which of these formulas solves the problem more accurately? In [9], this question is investigated using the Pearson criterion. This article describes the procedure and on its basis gives formulas available in literature and proposed new formulas using the entropy coefficient. A comparison is made with the previously published results of applying Pearson's concord criterion for these purposes. Differences in the estimates of the accuracy of the formulas are found. The proposed new formulas for calculating the number of intervals showed the best results. Calculations have been made to compare the work of the same formulas for the distribution of sample data according to the normal law and the Rayleigh law.

Keywords

• entropy coefficient
• grouping intervals number
• interval estimates
• Rayleigh distribution