ISSN 2234-8417 (Online) ISSN 1598-5857 (Print)

Table of Contents
2012's   30,3-4(May)
  On H$\grave{a}$jek-R$\grave{e}$nyi-type inequality for conditionally negatively associated random variables and its applications
    By HYE-YOUNG SEO ..........1339
Generic Number - 1339
References - 0
Written Date - May 15th, 12
Modified Date - May 15th, 12
Downloaded Counts - 78
Visited Counts - 791
Original File
Let $\{ \Omega, \mathcal{F}, P \}$ be a probability space and $\{X_n
| n \geq 1\}$ be a sequence of random variables defined on it. A
finite sequence of random variables $\{X_n | n \geq 1\}$
is said to be conditionally negatively associated given $\mathcal{F}$ if for every pair of disjoint
subsets $A$ and $B$ of $\{ 1, 2, \cdots, n \},$ $ Cov^{\mathcal{F}} (f_1 (X_i , i \in A), f_2
(X_j , j \in B))\leq 0 ~a.s.$
whenever $f_1$ and $f_2$ are coordinatewise nondecreasing functions. We extend the H$\grave
{a}$jek-R$\grave{e}$nyi-type inequality from negative association to
conditional negative association of random variables.
In addition, some corollaries are given.

학회 : 정보전산응용수학회(KSICAM) (구: KSCAM & Korean SIGCAM)
연구소 : SPCHIN 전산응용수학연구소 ( SPCHIN-CAM Institute : SPCHIN-CAMI)
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