On some relationships between records in the transition from continuous to discrete distributions
DOI:
https://doi.org/10.21638/spbu01.2022.203Abstract
In the present work, we consider discretization of continuous distributions and study relations between continuous record values, weak record values and discrete record values obtained from continuous record values by discretization. We first compare the numbers of continuous record values registered in real intervals and the numbers of discrete record values and weak record values located on the sets of non-negative integers. Further in the paper, we introduce the so-called strong continuous record values that hold out after discretization and we discuss their distributional properties. We also analyze what happens with record values after discretization of the standard exponential distribution. Finally, we present a simulation experiment, which supports the theoretical results of the paper.Keywords:
records, strong records, weak records, discretization, exponential distribution, geometric distribution
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References
Литература
1. Ahsanullah M. Record values theory and applications. University Press of America (2004).
2. Ahsanullah M., Nevzorov V. B. Record via Probability Theory. Atlantis Press (2015).
3. Arnold B., Balakrishnan N., Nagaraja H. Records. New York, Wiley (1998).
4. Невзоров В.Б. Рекорды. Математическая теория. Москва, Фазис (2000).
5. Shorrock R.W. A limit theorem for inter-record times. J. Appl. Probab. 9 (1), 219–223 (1972).
6. Shorrock R.W. On record values and record times. J. Appl. Probab. 9 (2), 316–326 (1972).
7. Степанов А.В. Предельные теоремы для слабых рекордов. Теория вероятн. и ее примен. 37 (3), 586–590 (1992).
References
1. Ahsanullah M. Record values theory and applications. University Press of America (2004).
2. Ahsanullah M., Nevzorov V. B. Record via Probability Theory. Atlantis Press (2015).
3. Arnold B., Balakrishnan N., Nagaraja H. Records. New York, Wiley (1998).
4. Nevzorov V. Rekordy. Matematicheskaja teorija. Moscow, Fazis Publ. (2000). (In Russian) [Eng. transl.: Nevzorov V. Records. Mathematical Theory. In Ser.: Translations of Mathematical Theory, vol. 194. AMS (2001)].
5. Shorrock R.W. A limit theorem for inter-record times. J. Appl. Probab. 9 (1), 219–223 (1972).
6. Shorrock R.W. On record values and record times. J. Appl. Probab. 9 (2), 316–326 (1972).
7. Stepanov A.V. Limit theorems for weak records. Teoriya Veroyatnostei i ee Primeneniya 37 (3), 586–590 (1992). (In Russian) [Eng. transl.: Theory Probab. Appl. 37 (3), 570–574 (1992)].
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Published
2022-07-06
How to Cite
Ahsanullah, M., Nevzorov, V. B., & Stepanov, A. V. (2022). On some relationships between records in the transition from continuous to discrete distributions. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 9(2), 209–218. https://doi.org/10.21638/spbu01.2022.203
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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.
