Abstract

Given independent random variables X1 , . . . , Xn, with continuous distributions F1 , . . . , Fn, we investigate the order in which these random variables should be arranged so as to minimize the number of upper records. We show that records are stochastically minimized if the sequence F1 , . . . , Fn decreases with respect to a partial order, closely related to the monotone likelihood ratio property. Also, the expected number of records is shown to be minimal when the distributions are comparable in terms of a one-sided hazard rate ordering. Applications to parametric models are considered.