Stochastic comparisons of order statistics and their concomitants

• Authors: Ismihan Bairamov;Baha-Eldin Khaledi;Moshe Shaked
• Venue: Journal of Multivariate Analysis
• Year: 2014

Let X"1":"n@?X"2":"n...@?X"n":"n be the order statistics from some sample, and let Y"["1":"n"],Y"["2":"n"],...,Y"["n":"n"] be the corresponding concomitants. One purpose of this paper is to obtain results that stochastically compare, in various senses, the random vector (X"r":"n,Y"["r":"n"]) to the random vector (X"r"+"1":"n,Y"["r"+"1":"n"]), r=1,2,...,n-1. Such comparisons are called one-sample comparisons. Next, let S"1":"n@?S"2":"n...@?S"n":"n be the order statistics constructed from another sample, and let T"["1":"n"],T"["2":"n"],...,T"["n":"n"] be the corresponding concomitants. Another purpose of this paper is to obtain results that stochastically compare, in various senses, the random vector (X"r":"n,Y"["r":"n"]) with the random vector (S"r":"n,T"["r":"n"]), r=1,2,...,n. Such comparisons are called two-sample comparisons. It is shown that some of the results in this paper strengthen previous results in the literature. Some applications in reliability theory are described.