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Record values of exponentially distributed random variables

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Abstract

A sequence {Xn, n≥1} of independent and identically distributed random variables with absolutely continuous (with respect to Lebesque measure) cumulative distribution function F(x) is considered. Xj is a record value of this sequence if Xj>max(X1,…,Xj−1), j>1. Let {XL(n), n≥0} with L(o)=1 be the sequence of such record values and Zn,n−1=XL(n)–XL(n−1). Some properties of Zn,n−1 are studied and characterizations of the exponential distribution are discussed in terms of the expectation and the hazard rate of zn,n−1.

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References

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Authors
  1. Mohammad Ahsanullah
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Ahsanullah, M. Record values of exponentially distributed random variables. Statistische Hefte 22, 121–127 (1964). https://doi.org/10.1007/BF02933548

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  • DOI: https://doi.org/10.1007/BF02933548

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