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On the total time spent in records by a discrete uniform sequence
Published online by Cambridge University Press: 14 July 2016
Abstract
We consider the sum Sd of record values in a sequence of independent random variables that are uniformly distributed on 1,…,d. This sum can be interpreted as the total amount of time spent in record lifetimes in the standard renewal theoretic setup. We investigate the distributional limit of Sd and some related quantities as d→∞. Some explicit values are given for d=6, a case that can be interpreted as a simple game of chance.
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- Copyright © by the Applied Probability Trust 2001
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