Dziubdziela, Wiesław; Tomicka-Stisz, Agata Stochastic ordering of random \(k\)th record values. (English) Zbl 0998.60050 Appl. Math. 26, No. 3, 293-298 (1999). 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 Keywords:extreme value theory; \(k\)-record values; random \(k\)-record values; random sums; hazard rate order; likelihood ratio order; stochastic comparison PDFBibTeX XMLCite \textit{W. Dziubdziela} and \textit{A. Tomicka-Stisz}, Appl. Math. 26, No. 3, 293--298 (1999; Zbl 0998.60050) Full Text: DOI EuDML