• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.55-63
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• 2001

In this paper, we derive a general strong law of large numbers and a general weak law of large number for normed weighted sums of pairwise negative quadrant dependent random variables with the common distribution function.

• Journal of the Korean Statistical Society
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• v.29 no.3
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• pp.261-268
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• 2000

Let {Xn,n$\geq$1} be a sequence of pairwise negative quadrant dependent(NQD) random variables and let {an,n$\geq$1} and {bn,n$\geq$1} be sequencesof constants such that an$\neq$0 and 0$\infty$. In this note, for pairwise NQD random varibles, a general weak law of alrge numbers of the form(∑│aj│Xj-$\upsilon$n)/bnlongrightarrow0) is established, where {νn,n$\geq$1} is a suitable sequence. AMS 2000 subject classifications ; 60F05

• Communications for Statistical Applications and Methods
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• v.7 no.1
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• pp.291-296
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• 2000

Petrov(1996) examined the connection between general moment conditions and the applicability of the strong law lf large numbers to a sequence of pairwise independnt and identically distributed random variables. In this note wee generalize Theorem 1 of Petrov(1996) and also show that still holds under assumption of pairwise negative quadrant dependence(NQD).

• Honam Mathematical Journal
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• v.33 no.2
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• pp.163-171
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• 2011

In this paper we provide extensions of the Marcinkiewicz Zygmund laws of large numbers for i.i.d random variables with multidimensional indices to the case of negatively dependent random fields.

• Honam Mathematical Journal
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• v.25 no.1
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• pp.117-127
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• 2003

In this note we perform an extreme point analysis on two natural definitions of negative quadrant dependence of three random variables and examine how different these two notions of dependence. We also characterize some special distributions which are both negatively lower orthant dependent and negatively upper orthant dependent.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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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.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.247-259
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• 2005

Necessary and sufficient conditions, under which there exists (at least) a sequence of vectors of real numbers for which the distribution function (d.f.) of any vector of extreme order statistics converges to a non-degenerate limit, are derived. The interesting thing is that these conditions solely depend on the univariate marginals. Moreover, the limit splits into the product of the limit univariate marginals if all the bivariate marginals of the trivariate d.f., from which the sample is drawn, is of negative quadrant dependent random variables (r.v.'s). Finally, all these results are stated for the multivariate extremes with arbitrary dimensions.

• Honam Mathematical Journal
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• v.21 no.1
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• pp.149-156
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• 1999

Let $\{X_n,\;n{\geq}1\}$ be a sequence of pairwise negative quadrant dependent (NQD) random variables which are stochastically dominated by X. Let $\{a_n,\;n{\geq}1\}$ and $\{b_n,\;n{\geq}1\}$ be sequences of constants such that $a_n>0$ and $0. In this note a weak law of large number of the form $({\sum}_{j=1}^na_jX_j-{\nu}_n)/b_n\rightarrow\limits^p0$ is established, where $\{{\nu}_n,\;n{\geq}1\}$ is a suitable sequence.

• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.1101-1111
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• 2008

Under the condition of h-integrability and appropriate conditions on the array of weights, we establish complete convergence and strong law of large numbers for weighted sums of an array of dependent random variables.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.831-839
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• 1996

In the last years there has been growing interest in concepts of positive (negative) dependence of stochastic processes such that concepts are considerable us in deriving inequalities in probability and statistics. Lehmann [7] introduced various concepts of positive(negative) dependence in the bivariate case. Stronger notions of bivariate positive(negative) dependence were later developed by Esary and Proschan [6]. Ahmed et al.[2], and Ebrahimi and Ghosh[5] obtained multivariate versions of various positive(negative) dependence as described by Lehmann[7] and Esary and Proschan[6]. Concepts of positive(negative) dependence for random variables have subsequently been extended to stochastic processes in different directions by many authors.