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MATHEMATICS
On some relationships between records in the transition from continuous to discrete distributions
M. Ahsanullaha, V. B. Nevzorovb, A. V. Stepanovc a Rider University, 2083 Lawrenceville Road, Lawrenceville, NJ, 08648, USA
b St Petersburg State University, 7-9, Universitetskaya nab., St Petersburg, 199034, Russian Federation
c Immanuel Kant Baltic Federal University, 14, ul. A.Nevskogo, Kaliningrad, 236041, Russian Federation
Abstract:
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.
Received: 17.10.2021 Revised: 29.11.2021 Accepted: 02.12.2021
Citation:
M. Ahsanullah, V. B. Nevzorov, A. V. Stepanov, “On some relationships between records in the transition from continuous to discrete distributions”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 9:2 (2022), 209–218; Vestn. St. Petersbg. Univ., Math., 9:2 (2022), 209–218
Linking options:
https://www.mathnet.ru/eng/vspua3 https://www.mathnet.ru/eng/vspua/v9/i2/p209
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Abstract page: | 57 | Full-text PDF : | 10 | References: | 18 |
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