Representations of ordered random variables in the terms of sums or products of independent variables
Abstract
Дан обзор имеющихся представлений, которые позволяют выразить такие зависимые упорядоченные величины, как порядковые статистики и рекорды, в виде сумм независимых слагаемых или произведений независимых случайных множителей. Получены некоторые новые соотношения подобного вида, которые таким же образом задают совместные распределения представителей этих двух типов упорядоченных случайных величин. Библиогр. 14 назв.
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References
1. Ahsanullah M., Nevzorov V.B. Order Statistics. Examples and Exercises. New York: Nova Science Publishers, 2005. 236 p.
2. Ahsanullah M., Nevzorov V.B., Shakil M. An introduction to order statistics. Atlantis Press, 2013. 244 p.
3. Arnold B.C., Balakrishnan N., Nagaraja H.N. Records. New York: John Wiley & Sons, 1998. 312 p.
4. Arnold B.C., Balakrishnan N., Nagaraja H.N. A first course in order statistics. New York: John Wiley & Sons, 1998. 277 p.
5. David H.A., Nagaraja H.N. Order statistics. Third edition. New York: John Wiley & Sons, 2003. 458 p.
6. Невзоров В.Б. Рекорды. Математическая теория. М.: Фазис, 2000. 244 c.
7. Sukhatme P.V. Tests of significance for samples of the χ2-population with two degrees of freedom // Ann. Eugen. 1937. N 8. P. 52-56.
8. Chandler K.N. The distribution and frequency of record values // J. R. Stat. Soc., Ser. B. 1952. Vol. 14. P. 220-228.
9. Foster F.G., Stuart A. Distribution free tests in time-series band on the breaking of records // Royal Statist. Soc. 1954. B16, N 1. P. 1-22.
10. Foster F.G., Teichroew D. A sampling experiment on the powers of the records tests for trend in a time series // J. Royal Statist. Soc. 1955. B17. P. 115-121.
11. Renyi A. Theorie des elements saillants d’une suite d’observations. Colloquim on combinatorial methods in probability theory, Math. Inst., Aarhus Univ., Aarhus, Denmark. August 1-10. 1962. P. 104-117; см. также: Selected papers of Alfred Renyi, vol. 3 (1976), Akademiai Kiado, Budapest. P. 50-65.
12. Stuart A. The efficiency of the record test for trend in normal regression // Journal of the Royal Statistical Society. Series B. 1957. Vol. 19. P. 149-153.
13. Malmquist S. On a property of order statistics from a rectangular distribution // Scand. Aktuar. 1950. Vol. 33. P. 214-222.
14. Lurie D., Hartley H.O. Machine-Generation of Order Statistics for Monte Carlo Computations // The American Statistician. 1972. Vol. 26, N 1. P. 26-27.
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Published
2020-08-20
How to Cite
Nevzorov, V. B. (2020). Representations of ordered random variables in the terms of sums or products of independent variables. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 3(4), 627–640. Retrieved from https://math-mech-astr-journal.spbu.ru/article/view/8668
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Mathematics
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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
