Geometric distribution of the k-th order

V.I. Glebov; S.Ya. Krivolapov

doi:10.18127/j20700814-202306-04

Geometric distribution of the k-th order

V.I. Glebov¹, S.Ya. Krivolapov²

research article UDC 519.213:51-77 Pages: 29-37 doi.org/10.18127/j20700814-202306-04

^1,2 Financial University under the Government of the Russian Federation (Moscow, Russia)

Keywords: Distributions of the Bernoulli test scheme recursive equations

Abstract

A generalization of the geometric distribution law is considered – the distribution law of a random variable equal to the step number in the sequence of tests according to the Bernoulli scheme, at which a series of k consecutive "successes" (k = 2, 3, …) falls for the first time. Expressions for the main probabilistic characteristics of a random variable are obtained.

Received: 09.08.2023
Approved after review: 23.08.2023
Accepted: 02.10.2023

How to cite

Глебов В.И., Криволапов С.Я. Геометрическое распределение k-го порядка // Информационно-измерительные и управляющие системы. 2023. № 6. С. 29–37. DOI: https://doi.org/10.18127/j20700814-202306-04

References

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[1] Feller V. Vvedenie v teoriyu veroyatnostei i ee prilozheniya. M.: Mir. 1984. T. 1. 528 s. (in Russian)

[2] Dzhonson N.L., Kots S., Kemp A. Odnomernye diskretnye raspredeleniya. M.: Binom. Laboratoriya znanii. 2014. 560 s. (in Russian)

[3] Philippou A.N., Muwafi A.A. Waiting for the Kth consecutive success and the Fibonacci sequence of the order K. Fibonacci Quarterly. February 1982. P. 28−32.

[4] Ivchenko G.I., Medvedev Yu.I. Diskretnye veroyatnostnye modeli. M.: DLENAND. 2021. 620 s. (in Russian)

[5] Leeuw K. de, Moore E., Shannon C., Shapiro N. Computability by Probabilistic Machines. In: Automata Studies. Ed. by C. Shannon and J. McCarthy. Princeton University Press. 1956. P. 183−212.

[6] Gill J. Probabilistic Turing Machines and Complexity of Computations. PhD thesis. U.C. Berkeley. 1972. P. 85−103.

[7] Gill J. Computational Complexity of Probabilistic Turing Machines. SIAM J. Comput. 6.4 (1977). P. 675−695.
url: http://dx.doi.org/10. 1137/0206049.

[8] Makhnist L.P., Karimova T.I., Gladkii I.I., Rubanov V.S. Momenty raspredeleniya veroyatnostei i nekotorye tselochislennye posledovatelnosti. Vestnik Brestskogo gosudarstvennogo tekhnicheskogo universiteta. 2013. № 5. S. 54−56. (in Russian)