Methods for identification of probability distribution of random variables from data samples with R statistical computing language
The corresponding data set used to illustrate the above methods was taken from probability distribution of the maximum of Chenstov field restriction to a particular curve. The distribution was simulated with the special original algorithm in R statistical software.
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Chentsov, N. N. (1956). Wiener random fields depending on several parameters [in Russian]. Doklady Akademii Nauk SSSR, 106(4), 607–609.
The Comprehensive R Archive Network. (n.d.). https://cran.cnr.berkeley.edu/
Cramér, H. (1946). Mathematical methods of statistics. Princeton, NJ: Princeton University Press.
Dykhovychnyi, O. O., & Kruglova, N. V. (2018). Simulation of a gaussian process with correlation function of a special form. In Abstracts of International conference "Stochastic Equations, Limit Theorems and Statistics of Stochastic Processes dedicated to the 100th anniversary of I. I. Gikhman, 2018, September 17–22, Kyiv, Ukraine (pp. 18–19). http://matan.kpi.ua/gikhman100conf/g100-abstracts.pdf
Kobzar, A. I. (2006). Applied mathematical statistics [in Russian]. Moscow: Fizmatlit.
Lapko, A. V., Chentsov, S. V., Krokhov, S. I., & Feldman, L. A. (1996). Self-learning systems for information processing and decision making [in Russian]. Novosibirsk: Nauka.
Park, C., & Paranjape, S. R. (1974). Probabilities of Wiener paths crossing differentiable curves. Pacific journal of mathematics, 53(2), 579–583. https://projecteuclid.org/euclid.pjm/1102911625
Syzrantsev, V. N., Nevelev, Y. P., & Golofast, S. L. (2006). Adaptive method for probability density function reconstruction [in Russian]. Proceedings of Higher Educational Institutions. Machine Building, 2006(12), 3–11.
Wolfowitz, J. (1957). The minimum distance method. The Annals of Mathematical Statistics, 28(1), 75–88. https://doi.org/10.1214/aoms/1177707038
Wolverton, C. T., & Wagner, T. J. (1969). Asymptotically optimal discriminant functions for pattern classifi cation. IEEE Transactions on Information Theory, 15(2), 258–265. https://doi.org/10.1109/TIT.1969.1054295
Yeh, J. (1960). Wiener measure in a space of functions of two variables. Transactions of the American Mathematical Society, 95(3), 433–450. https://doi.org/10.1090/S0002-9947-1960-0125433-1
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