Order statistics with multivariate concomitants: stochastic comparisons
Article
Amini-Seresht, E, Khaledi, BE, Shaked, M. (2016). Order statistics with multivariate concomitants: stochastic comparisons
. STATISTICS, 50(1), 190-205. 10.1080/02331888.2015.1022550
Amini-Seresht, E, Khaledi, BE, Shaked, M. (2016). Order statistics with multivariate concomitants: stochastic comparisons
. STATISTICS, 50(1), 190-205. 10.1080/02331888.2015.1022550
Let (Formula presented.) , (Formula presented.) , be a sequence of independent and identically distributed (Formula presented.) -dimensional random vectors. Furthermore, let (Formula presented.) be the order statistics based on the first coordinates of the first n elements in the sequence, and let (Formula presented.) be the corresponding k-dimensional concomitants. Several results that compare (Formula presented.) and (Formula presented.) , with respect to various multivariate stochastic orders, are obtained. Next, let (Formula presented.) , (Formula presented.) , be another sequence of independent and identically distributed (Formula presented.) -dimensional random vectors. Furthermore, let (Formula presented.) be the order statistics based on the first coordinates of the first m elements in the sequence, and let (Formula presented.) be the corresponding k-dimensional concomitants. Several results that compare (Formula presented.) and (Formula presented.) , with respect to various multivariate stochastic orders, are established. It is shown that some of the results in this paper strengthen previous results in the literature. An application in reliability theory is described. A derivation of computable bounds, on various probabilistic quantities of interest involving multivariate concomitants, illustrates the theory.
