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Majorization bounds for distribution function | Ismihan Bairamov
; | Date: |
1 Sep 2011 | Abstract: | Let $X$ be a random variable with distribution function $F,$ and
$X_{1},X_{2},...,X_{n}$ are independent copies of $X.$ Consider the order
statistics $X_{i:n},$ $i=1,2,...,n$ and denote $F_{i:n}(x)=P{X_{i:n}leq x}.$
Using majorization theory we write upper and lower bounds for $F$ expressed in
terms of mixtures of distribution functions of order statistics, i.e. $sum
limits_{i=1}^{n}p_{i}F_{i:n}$ and $sum limits_{i=1}^{n}p_{i}F_{n-i+1:n}.$ 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 $m
ightarrowinfty.$ | Source: | arXiv, 1109.0141 | Services: | Forum | Review | PDF | Favorites |
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