• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.37-49
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• 1999

We derive the almost sure convergence for weighted sums of random variables which are either pairwise positive quadrant dependent or pairwise positive quadrant dependent or pairwise negative quadrant dependent and then apply this result to obtain the almost sure convergence of weighted averages. e also extend some results on the strong law of large numbers for pairwise independent identically distributed random variables established in Petrov to the weighted sums of pairwise negative quadrant dependent random variables.

• Communications for Statistical Applications and Methods
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• v.19 no.2
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• pp.247-256
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• 2012

In this paper we prove the complete convergence for weighted sums of pairwise negatively quadrant dependent random variables. Some results on identically distributed and negatively associated setting of Liang and Su (1999) are generalized and extended to the pairwise negative quadrant dependence case.

• 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.

• 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).

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.885-893
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• 2009

In this paper we study the strong law of large numbers for weighted average of pairwise negatively quadrant dependent random variables. This result extends that of Jamison et al.(Convergence of weight averages of independent random variables Z. Wahrsch. Verw Gebiete(1965) 4 40-44) to the negative quadrant dependence.

• 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

• 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.