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Stochastic ordering of random \(k\)th record values. (English) Zbl 0998.60050

Summary: Let \(X_1,X_2,\ldots\) be a sequence of independent and identically distributed random variables with continuous distribution function \(F(x)\). Denote by \(X(1,k),X(2,k),\ldots\) the \(k\)th record values corresponding to \(X_1,X_2,\ldots\) We obtain some stochastic comparison results involving the random \(k\)th record values \(X(N,k)\), where \(N\) is a positive integer-valued random variable which is independent of the \(X_i\).

MSC:

60G70 Extreme value theory; extremal stochastic processes
60E15 Inequalities; stochastic orderings
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