2011/09/07 by Ismihan Bairamov, Bairamov, Ismihan
Mathematics · #62G30 #62G70 #FOS: Mathematics #Mathematical Inequalities and Applications #Mathematical functions and polynomials #Statistical Distribution Estimation and Applications #Statistics Theory (math.ST) #math.ST #msc:62G30 #msc:62G70 #stat.TH
paper · pdf · doi:10.48550/arxiv.1109.1477
7 pages
arxiv created 2011/09/07 · openalex publication_date 2011/09/07 · arxiv updated 2011/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let (X,Y) be a random vector with distribution function F(x,y), and (X1,Y1),(X2,Y2),...,(Xn,Yn) are independent copies of (X,Y). Let Xi:n be the ith order statistics constructed from the sample X1,X2,...,Xn of the first coordinate of the bivariate sample and Y[i:n] be the concomitant of Xi:n. Denote Fi:n% (x,y)=P\Xi:n≤ x,Y[i:n]≤ y\. Using majorization theory we write upper and lower bounds for F expressed in terms of mixtures of joint distributions of order statistics and their concomitants, i.e. \dsum i=1n% ∑i=1n piFi:n(x,y) and \dsum i=1n% ∑i=1n piFn-i+1:n(x,y). It is shown that these bounds converge to F for a particular sequence (p1(m),p2(m),...,pn(m)),m=1,2,.. as m→∞.