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Record values and the exponential distribution

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Abstract

A sequence {X n,n≧1} of independent and identically distributed random variables with continuous cumulative distribution functionF(x) is considered.X j is a record value of this sequence ifX j>max (X 1, …,X j−1). Let {X L(n) n≧0} be the sequence of such record values. Some properties ofX L(n) andX L(n)−XL(n−1) are studied when {X n,n≧1} has the exponential distribution. Characterizations of the exponential distribution are given in terms of the sequence {X L(n),n≧0}

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References

  1. Karlin, S. (1966).A First Course in Stochastic Processes, Academic Press, N.Y.

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Authors and Affiliations

  1. Health and Welfare Canada, Ottawa

    M. Ahsanullah

Authors
  1. M. Ahsanullah
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Additional information

The work was partly completed when the author was at the Department of Statistics, University of Brasilia, Brazil.

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Ahsanullah, M. Record values and the exponential distribution. Ann Inst Stat Math 30, 429–433 (1978). https://doi.org/10.1007/BF02480233

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  • DOI: https://doi.org/10.1007/BF02480233

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