• 제목/요약/키워드: Negatively associated random variables

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A NOTE ON THE STRONG LAW OF LARGE NUMBERS FOR WEIGHTED SUMS OF NEGATIVELY DEPENDENT RANDOM VARIABLES

  • Lee, S.W.;Kim, T.S.;Kim, H.C.
    • 대한수학회논문집
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    • 제13권4호
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    • pp.855-863
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    • 1998
  • Some conditions on the strong law of large numbers for weighted sums of negative quadrant dependent random variables are studied. The almost sure convergence of weighted sums of negatively associated random variables is also established, and then it is utilized to obtain strong laws of large numbers for weighted averages of negatively associated random variables.

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ON THE COMPLETE CONVERGENCE FOR WEIGHTED SUMS OF NEGATIVELY SUPERADDITIVE DEPENDENT RANDOM VARIABLES

  • SEO, HYE-YOUNG;SHII, DA-LI;BAEK, JONG-IL
    • Journal of applied mathematics & informatics
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    • 제37권3_4호
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    • pp.207-217
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    • 2019
  • We are presented of several basic properties for negatively superadditive dependent(NSD) random variables. By using this concept we are obtained complete convergence for maximum partial sums of rowwise NSD random variables. These results obtained in this paper generalize a corresponding ones for independent random variables and negatively associated random variables.

A STRONG LAW OF LARGE NUMBERS FOR AANA RANDOM VARIABLES IN A HILBERT SPACE AND ITS APPLICATION

  • Ko, Mi-Hwa
    • 호남수학학술지
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    • 제32권1호
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    • pp.91-99
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    • 2010
  • In this paper we introduce the concept of asymptotically almost negatively associated random variables in a Hilbert space and obtain the strong law of large numbers for a strictly stationary asymptotically almost negatively associated sequence of H-valued random variables with zero means and finite second moments. As an application we prove a strong law of large numbers for a linear process generated by asymptotically almost negatively random variables in a Hilbert space with this result.

Complete convergence for weighted sums of AANA random variables

  • 김태성;고미화
    • 한국통계학회:학술대회논문집
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    • 한국통계학회 2002년도 추계 학술발표회 논문집
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    • pp.209-213
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    • 2002
  • We study maximal second moment inequality and derive complete convergence for weighted sums of asymptotically almost negatively associated(AANA) random variables by applying this inequality. 2000 Mathematics Subject Classification : 60F05

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THE ALMOST SURE CONVERGENCE FOR THE IDENTICALLY DISTRIBUTED NEGATIVELY ASSOCIATED RANDOM VARIABLES WITH INFINITE MEANS

  • Kim, Hyun-Chull
    • Journal of applied mathematics & informatics
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    • 제28권1_2호
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    • pp.363-372
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    • 2010
  • In this paper we prove the almost sure convergence of partial sums of identically distributed and negatively associated random variables with infinite expectations. Some results in Kruglov[Kruglov, V., 2008 Statist. Probab. Lett. 78(7) 890-895] are considered in the case of negatively associated random variables.

COMPLETE CONVERGENCE FOR ARRAYS OF ROWWISE ASYMPTOTICALLY NEGATIVELY ASSOCIATED RANDOM VARIABLES

  • Kim, Hyun-Chull
    • 충청수학회지
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    • 제30권4호
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    • pp.411-422
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    • 2017
  • Let {$X_{ni}$, $i{\geq}1$, $n{\geq}1$} be an array of rowwise asymptotically negatively associated random variables and {$a_{ni}$, $i{\geq}1$, $n{\geq}1$} an array of constants. Some results concerning complete convergence of weighted sums ${\sum}_{i=1}^{n}a_{ni}X_{ni}$ are obtained. They generalize some previous known results for arrays of rowwise negatively associated random variables to the asymptotically negative association case.