On some relations which tie exponential and geometrical record random variables

Authors

  • Sergey M. Ananjevskii St. Petersburg State University, 7–9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
  • Valery B. Nevzorov St. Petersburg State University, 7–9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation

DOI:

https://doi.org/10.21638/spbu01.2021.101

Abstract

Different record achievements are fixed in many domains of the human activities. Very often this process happens with some rate of discretization (up to seconds, up to meters or up to thousands of individuals) of the observed results. On the examples of exponential and geometrical distributions it is shown how such type of the transition from continuous to discrete distributions can vary the numbers of the record values in the corresponding sequences of the random variables.

Keywords:

exponential distributions, geometrical distributions, record times, record values, weak records

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References

Литература

1. Ahsanullah M. Record values-theory and applications. University Press of America (1984).

2. Ahsanullah M., Nevzorov V.B. Records via probability theory. In: Atlantis Studies in Probability and Statistics. Atlantis Press (2015).

3. Arnold B.C., Balakrishnan N., Nagaraja H.N. Records. New York, John Wiley & Sons (1998).

4. Невзоров В.Б. Рекорды. Математическая теория. Москва, Фазис (2000).

5. Невзоров В.Б. Сравнение числа рекордов в последовательностях дискретных и непрерывных случайных величин. Вестник Санкт-Петербургского университета. Математика. Механика. Астрономия 4 (62), вып. 3, 459–465 (2017). https://doi.org/10.21638/11701/spbu01.2017.308

References

1. Ahsanullah M. Record values-theory and applications. University Press of America (1984).

2. Ahsanullah M., Nevzorov V.B. Records via probability theory. In: Atlantis Studies in Probability and Statistics. Atlantis Press (2015).

3. Arnold B.C., Balakrishnan N., Nagaraja H.N. Records. New York, John Wiley & Sons (1998).

4. Nevzorov V.B. Rekordy. Matematicheskaia teoriia. Moscow, Fazis Publ. (2000). (In Russian) [Engl. transl.: Nevzorov V.B. Records. Mathematical theory. In: Translations of Mathematical Monographs, vol. 194. AMS (2001)].

5. Nevzorov V.B. Comparison of numbers of records in the sequences of discrete andcontinuous random variables. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 4 (62), iss. 3, 459–465 (2017). https://doi.org/10.21638/11701/spbu01.2017.308 (In Russian) [Engl. transl.: Vestnik St. Petersb. Univ. Math. 50, iss. 3, 282–286 (2017). https://doi.org/10.3103/S1063454117030116].

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Published

2021-05-29

How to Cite

Ananjevskii, S. M., & Nevzorov, V. B. (2021). On some relations which tie exponential and geometrical record random variables. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 8(1), 3–11. https://doi.org/10.21638/spbu01.2021.101

Issue

Vol. 8 No. 1 (2021)

Section

Mathematics

License

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.