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.
References
Hald A. Matematicheskaya statistika s tekhnicheskimi prilozheniyami [Mathematical statistics with technical applications]. Moskow, Izd-vo inostr. lit, 1956.
Sturges H. A. The choice of a class interval. JASA, 1926, vol. 21, рр. 65-66.
Mann H. B., Wald A. On the choice of the number of intervals in the application of the chi-square test. Ann. Math. Statist, 1942, vol. 13, рр. 478-479.
Smirnov N. V. [On the construction of a confidence domain for the distribution density of a random variable]. Doklady Akademii Nauk SSSR, 1950, vol. 74, no 2, pp. 189-192 (Rus)
Scott D. W. On optimal and data-based histograms. Biometrika, 1979, vol. 66, pp. 605-610.
Livshits M. E., Ivanov-Muromsky K. A., Zaslavsky S. Ya., Voitinsky E. Ya., Lerner V. F, Romm B. I. Chislovye metody analiza sluchainyh protsesov [Numerical methods of analysis of random processes]. Moscow, Nauka, 1976. (Rus)
Novitsky P. V., Zograf I. A. Otcenka pogreshnostei resultatov ismerenii [Estimation of errors in measurement results]. Leningrad, Energoatomizdat, 1991. (Rus)
Bulashev S. V. Statistika dlya treiderov [Statistics for traders]. Moscow, Sputnik company+, 2003. (Rus)
Kalmykov V. V., Antonyuk F. I., Zenkin N. V. [Determination of the optimal number of classes of grouping of experimental data for interval estimates]. Yuzhnosibirskii nauchnyi vestneyk, 2014, no 3, pp. 56-58. (Rus)
Novitsky, P. V. [The concept of the entropy value of error]. Izmeritel`naya tekhnika, 1966, no 7, pp. 11-14. (Rus)
