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- W1673959164 abstract "Let ($X,Y)$ be a random vector with distribution function $F(x,y),$ and $(X_{1},Y_{1}),(X_{2},Y_{2}),...,(X_{n},Y_{n})$ are independent copies of ($X,Y).$ Let $X_{i:n}$ be the $i$th order statistics constructed from the sample $X_{1},X_{2},...,X_{n}$ of the first coordinate of the bivariate sample and $Y_{[i:n]}$ be the concomitant of $X_{i:n}.$ Denote $F_{i:n}% (x,y)=P{X_{i:n}leq x,Y_{[i:n]}leq y}.$ 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. ${dsum limits_{i=1}^{n}}% {sumlimits_{i=1}^{n}} p_{i}F_{i:n}(x,y)$ and ${dsum limits_{i=1}^{n}}% {sumlimits_{i=1}^{n}} p_{i}F_{n-i+1:n}(x,y).$ It is shown that these bounds converge to $F$ for a particular sequence $(p_{1}(m),p_{2}(m),...,p_{n}(m)),m=1,2,..$ as $mrightarrowinfty.$" @default.
- W1673959164 created "2016-06-24" @default.
- W1673959164 creator A5020557526 @default.
- W1673959164 date "2011-09-07" @default.
- W1673959164 modified "2023-09-27" @default.
- W1673959164 title "Concomitants and majorization bounds for bivariate distribution function" @default.
- W1673959164 cites W2105809623 @default.
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