Geodesic
The method of selecting the best distribution law for continuous random variables on the basis of inverse mapping
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 9 (2017) no. 1, pp. 31-38 Cet article a éte moissonné depuis la source Math-Net.Ru

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The article describes a new method of identification of the law of distribution of a continuous random variable. The method is based on the selection from a given set of models of the distributions of such law distribution, which would be most consistent with the experimental data sample. The idea of the method is a continuous mapping of an empirical sampling distribution into the standard line. For each distribution model the functional value is determined. It is equal to the RMS error value is displayed into standard line. As a result, as the most probable law for initial sampling researchers select the law for which the corresponding value of the functional will be minimum. The examples of the method implementation using statistical tests based on a Monte-Carlo technique are given.
Keywords: random variable, distribution law, random sampling, statistical tests based on a Monte-Carlo method
Mots-clés : identification, test for concordance. 
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     title = {The method of selecting the best distribution law for continuous random variables on the basis of inverse mapping},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
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A. N. Tyrsin. The method of selecting the best distribution law for continuous random variables on the basis of inverse mapping. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 9 (2017) no. 1, pp. 31-38. http://geodesic.mathdoc.fr/item/VYURM_2017_9_1_a3/

[1] Korolyuk V. S., Portenko N. I., Skorokhod A. V., Turbin A. F., Handbook of Probability Theory and Mathematical Statistics, Nauka Publ., M., 1985, 640 pp. (in Russ.)

[2] Lemeshko B. Yu., Metrologiya, 2004, no. 7, 8–17 (in Russ.)

[3] Kendall M., Stuart A., Statistical inference and communication, Nauka Publ., M., 1973, 899 pp. (in Russ.)

[4] Cramer H., Mathematical Methods of Statistics, Mir Publ., M., 1975, 648 pp. (in Russ.)

[5] Lehmann E., Testing of Statistical Hypotheses, Nauka Publ., M., 1979, 408 pp. (in Russ.)

[6] Wilks S., Mathematical Statistics, Nauka Publ., M., 1967, 632 pp. (in Russ.)

[7] Ivchenko G. I., Medvedev Yu. I., Introduction to Mathematical Statistics, LKI Publ., M., 2010, 600 pp. (in Russ.)

[8] Tarasenko F. P., Nonparametric statistics, Izd-vo TGU Publ., Tomsk, 1976, 294 pp. (in Russ.)

[9] Katkovnik V. Ya., Non-parametric identification and data smoothing, Nauka Publ., M., 1985, 336 pp. (in Russ.)

[10] Devroy L., D'erfi L., Nonparametric density estimation (The $L_1$-approach), Mir Publ., M., 1988, 408 pp. (in Russ.)

[11] Karandeev D. A., Eysymont I. M., Upravlenie bol'shimi sistemami, 1 (1998), 48–57 (in Russ.)

[12] Yashin A. V., Lotonov M. A., Izmeritel'naya tekhnika, 2003, no. 3, 3–5 (in Russ.)

[13] Novitskiy P. V., Fundamentals of information theory of measurement devices, Energiya Publ., L., 1968, 248 pp. (in Russ.)

[14] Klyavin I. A., Tyrsin A. N., Avtometriya, 49:1 (2013), 18–25 (in Russ.)

[15] Magnus Ya. R., Katyshev P. K., Peresetskiy A. A., Econometrics. Initial course, Delo Publ., M., 2004, 576 pp. (in Russ.)

[16] Panyukov A. V., Tyrsin A. N., Izvestiya Chelyabinskogo nauchnogo tsentra, 2007, no. 1(35), 6–11 (in Russ.)

[17] Ermakov S. M., The Monte Carlo method and related questions, Nauka Publ., M., 1975, 472 pp. (in Russ.)

[18] Lemeshko B. Yu., Pomadin S. S., Sib. Zh. Ind. Mat., 5:3 (2002), 115–130 (in Russ.)