• 대한수학회보
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• 제57권3호
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• pp.607-622
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• 2020

In the paper, some probability convergence properties of series for rowwise sums of negatively superadditive dependent (NSD) random variables are discussed. We establish some sharp results on these convergence for NSD random variables under some general settings, which generalize and improve the corresponding ones of some known literatures.

• 대한수학회지
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• 제42권5호
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• pp.949-957
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• 2005

For weighted sum of a sequence {X, X$\_{n}$, n $\geq$ 1} of identically distributed, negatively orthant dependent random variables such that |r| > 0, has a finite moment generating function, a strong law of large numbers is established.

• 충청수학회지
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• 제28권3호
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• pp.409-417
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• 2015

In this paper, some $L_p$-convergences and complete convergences of the maximum of the partial sum for negatively superadditive dependent random variables are obtained. The proofs of the results are based on a new Rosenthal type inequality concerning negatively superadditive dependent random variables.

• Journal of applied mathematics & informatics
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• 제12권1_2호
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• pp.299-305
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• 2003

The central limit theorems are obtained for stationary linear processes of the form Xt = (equation omitted), where {$\varepsilon$t} is a strictly stationary sequence of random variables which are either linearly positive quad-rant dependent or associated and {aj} is a sequence of .eat numbers with (equation omitted).

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.441-453
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• 2005

In this article we will introduce a real valued random field on a restricted indexed set and construct a classical asymptotic limit theorems on them. We will survey the basic properties of weakly dependent random processes and investigate two major mixing conditions for sequences of random variables. The concepts of weakly dependent sequence of random variables will be generalized to the case of random fields. Finally we will construct a central limit theorem and prove it.

• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.603-610
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• 2006

In this paper we discuss the complete convergence of the linear process generated by negatively orthant dependent random variables under suitable conditions.

• 대한수학회논문집
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• 제14권3호
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• pp.597-609
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• 1999

In this article we prove a central limit theorem for strictly stationary weakly dependent random fields with some interlaced mix-ing conditions. Mixing coefficients are not assumed. The result it basically the same to Peligrad([4]), which is CLT weakly depen-dent arrays of random variables. The proof is quite similar to the of Peligrad.

• Communications for Statistical Applications and Methods
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• 제26권3호
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• pp.261-272
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• 2019

In this paper, we propose a procedure to build a prediction interval of the sum of dependent binary random variables over a graph to account for the dependence among binary variables. Our main interest is to find a prediction interval of the weighted sum of dependent binary random variables indexed by a graph. This problem is motivated by the prediction problem of various elections including Korean National Assembly and US presidential election. Traditional and popular approaches to construct the prediction interval of the seats won by major parties are normal approximation by the CLT and Monte Carlo method by generating many independent Bernoulli random variables assuming that those binary random variables are independent and the success probabilities are known constants. However, in practice, the survey results (also the exit polls) on the election are random and hardly independent to each other. They are more often spatially correlated random variables. To take this into account, we suggest a spatial auto-regressive (AR) model for the surveyed success probabilities, and propose a residual based bootstrap procedure to construct the prediction interval of the sum of the binary outcomes. Finally, we apply the procedure to building the prediction intervals of the number of legislative seats won by each party from the exit poll data in the $19^{th}$ and $20^{th}$ Korea National Assembly elections.

• 대한수학회보
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• 제56권4호
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• pp.1007-1025
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• 2019

In the present work, the complete convergence and complete moment convergence properties for arrays of rowwise extended negatively dependent (END) random variables are investigated. Some sharp theorems on these strong convergence for weighted sums of END cases are established. These main results not only generalize the known corresponding ones of Cai [2], Wang et al. [17] and Shen [14], but also improve them, respectively.

• Journal of applied mathematics & informatics
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• 제39권1_2호
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• pp.145-153
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• 2021

When {Xni|1 ≤ i ≤ n, n ≥ 1} be an array of rowwise negatively superadditive dependent(NSD) for semi-Gaussian random variables and {ani|1 ≤ i ≤ n, n ≥ 1} is an array of constants, we study the almost sure convergence of weighted sums ∑ni=1 aniXni under some appropriate conditions and we obtain some corollaries.