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Record values of exponentially distributed random variables
Authors:Mohammad Ahsanullah
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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