On the Number of Records in an iid Discrete Sequence

Eric S. Key ()
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Eric S. Key: University of Wisconsin - Milwaukee

Journal of Theoretical Probability, 2005, vol. 18, issue 1, 99-107

Abstract: The problem of the rate of growth of the number of record values and weak record values in an iid sequence of integer valued random variables is attacked as a perturbation of the case for continuous random variables. Conditions in terms of either the underlying probability mass function or the hazard function of the underlying distribution are given for the rate of growth of the number of records to be log(n) almost surely. The record problem has been considered by Gouet et al.(2001) [Adv. Appl. Prob. 33, 473-864] and by Vervaat(1973) [Stochastic processes Appl. 1, 317-334]. The results for records overlap those found in the former paper. The methods here are more elementary, and the results on weak records are not mentioned there. This paper improves on what may be derived from results in Vervaat. (1973) [Stochastic Processes Appl. 1, 317-334]

Keywords: Record values; weak record values; strong limits; discrete distributions; discrete hazard function (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s10959-004-2578-2

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