• Journal of the Korean Statistical Society
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• 제12권1호
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• pp.10-17
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• 1983

Let $X^{(n)}_j, j=1,2,\cdots,n, n=1,2,\cdots$ be a triangular array of random variables which arise naturally in a study of ferromagnetism in statistical mechanics. This paper presents weak convergence of random function $W_n(t)$, an appropriately normalized partial sum process based on $S^{(n)}_n = X^{(n)}_i+\cdot+X^{(n)}_n$. The limiting process W(t) is shown to be Gaussian when weak dependence exists. At the critical point where the change form weak to strong dependence takes place, W(t) turns out to be non-Gaussian. Our results are direct extensions of work by Ellis and Newmam (1978). An example is considered and the relation of these results to critical phenomena is briefly explained.

• Communications for Statistical Applications and Methods
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• 제6권2호
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• pp.585-594
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• 1999

Let {$X_{nj}$, 1$\leq$j$\leq$n,j$\geq$1} be a triangular array of random variables which are neither independent nor identically distributed. The almost sure convergences of randomly weighted partial sums of the form $$\sum_n^{j=1}$$ $W_{nj}$$X_{nj} are studied where {Wnj 1$\leq$j$\leq$n, j$\geq$1} is a triangular array of random weights. Application regarding the Efron bootstrap is also introduced.

• 한국경영과학회지
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• 제19권1호
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• pp.85-98
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• 1994

The distribution of random sum of i. i. d. exponential random variables is called GHP (Generalized Phase-Type) distribution. The class of GPH distributions is large enough to include PH (Phase-Type) distributions and has several properties which can be applied conveniently for computational purposes. In this paper, we show that any distribution difined on R$^{+}$ can be app-roximated by the GPH distribution and demonstrate the accuracy of the approximation through various numerical examples. Also, we introduce an efficient way to compute the delay and waiting various numerical examples. Also, we introduce an efficient way to compute the delay and waiting time distributions of the GPH/GPH/1 queueing system which can be used as an approximation model for the GI/G/1 system, and validate its accuracy through numerical examples. The theoretical and experimental results of this paper help us accept the usefulness of the approximations based on GPH distribution.n.

• Communications for Statistical Applications and Methods
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• 제16권5호
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• pp.841-849
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• 2009

Let {$X_n$, n ${\ge}$ 1} be a negatively associated sequence of identically distributed random variables with mean zeros and positive finite variances. Set $S_n$ = ${\Sigma}^n_{i=1}\;X_i$. Suppose that 0 < ${\sigma}^2=EX^2_1+2{\Sigma}^{\infty}_{i=2}\;Cov(X_1,\;X_i)$ < ${\infty}$. We prove that, if $EX^2_1(log^+{\mid}X_1{\mid})^{\delta}$ < ${\infty}$ for any 0< ${\delta}{\le}1$, then $\lim_{{\epsilon}\downarrow0}{\epsilon}^{2{\delta}}\sum_{{n=2}}^{\infty}\frac{(logn)^{\delta-1}}{n^2}ES^2_nI({\mid}S_n{\mid}\geq{\epsilon}{\sigma}\sqrt{nlogn}=\frac{E{\mid}N{\mid}^{2\delta+2}}{\delta}$, where N is the standard normal random variable. We also prove that if $S_n$ is replaced by $M_n=max_{1{\le}k{\le}n}{\mid}S_k{\mid}$ then the precise rate still holds. Some results in Fu and Zhang (2007) are improved to the complete moment case.

• International journal of advanced smart convergence
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• 제10권1호
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• pp.75-81
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• 2021

As the number of connected smart devices and applications increases explosively, the existing orthogonal multiple access (OMA) techniques have become insufficient to accommodate mobile traffic, such as artificial intelligence (AI) and the internet of things (IoT). Fortunately, non-orthogonal multiple access (NOMA) in the fifth generation (5G) mobile networks has been regarded as a promising solution, owing to increased spectral efficiency and massive connectivity. In this paper, we investigate the achievable data rate for non-orthogonal multiple access (NOMA) with negatively-correlated information sources (CIS). For this, based on the linear transformation of independent random variables (RV), we derive the closed-form expressions for the achievable data rates of NOMA with negatively-CIS. Then it is shown that the achievable data rate of the negatively-CIS NOMA increases for the stronger channel user, whereas the achievable data rate of the negatively-CIS NOMA decreases for the weaker channel user, compared to that of the positively-CIS NOMA for the stronger or weaker channel users, respectively. We also show that the sum rate of the negatively-CIS NOMA is larger than that of the positively-CIS NOMA. As a result, the negatively-CIS could be more efficient than the positively-CIS, when we transmit CIS over 5G NOMA networks.

• 호남수학학술지
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• 제31권3호
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• pp.369-380
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• 2009

Let $X,X_1,X_2,\;{\cdots}$ be identically distributed and negatively associated random variables with mean zeros and positive, finite variances. We prove that, if $E{\mid}X_1{\mid}^r$ < ${\infty}$, for 1 < p < 2 and r > $1+{\frac{p}{2}}$, and $lim_{n{\rightarrow}{\infty}}n^{-1}ES^2_n={\sigma}^2$ < ${\infty}$, then $lim_{{\epsilon}{\downarrow}0}{\epsilon}^{{2(r-p}/(2-p)-1}{\sum}^{\infty}_{n=1}n^{{\frac{r}{p}}-2-{\frac{1}{p}}}E\{{{\mid}S_n{\mid}}-{\epsilon}n^{\frac{1}{p}}\}+={\frac{p(2-p)}{(r-p)(2r-p-2)}}E{\mid}Z{\mid}^{\frac{2(r-p)}{2-p}}$, where $S_n\;=\;X_1\;+\;X_2\;+\;{\cdots}\;+\;X_n$ and Z has a normal distribution with mean 0 and variance ${\sigma}^2$.

• Communications for Statistical Applications and Methods
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• 제17권4호
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• pp.507-513
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• 2010

Let {$X_i,-{\infty}$ < 1 < $\infty$} be a doubly infinite sequence of identically distributed and negatively associated random variables with mean zero and finite variance and {$a_i,\;-{\infty}$ < i < ${\infty}$} be an absolutely summable sequence of real numbers. Define a moving average process as $Y_n={\sum}_{i=-\infty}^{\infty}a_{i+n}X_i$, n $\geq$ 1 and $S_n=Y_1+{\cdots}+Y_n$. In this paper we prove that E|$X_1$|$^rh$($|X_1|^p$) < $\infty$ implies ${\sum}_{n=1}^{\infty}n^{r/p-2-q/p}h(n)E{max_{1{\leq}k{\leq}n}|S_k|-{\epsilon}n^{1/p}}{_+^q}<{\infty}$ and ${\sum}_{n=1}^{\infty}n^{r/p-2}h(n)E{sup_{k{\leq}n}|k^{-1/p}S_k|-{\epsilon}}{_+^q}<{\infty}$ for all ${\epsilon}$ > 0 and all q > 0, where h(x) > 0 (x > 0) is a slowly varying function, 1 ${\leq}$ p < 2 and r > 1 + p/2.

• Journal of the Korean Data and Information Science Society
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• 제28권1호
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• pp.1-10
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• 2017

경시적 자료를 이용한 아동 학업성취도에 영향을 주는 요인을 찾기 위한 기존의 분석들은 각 아동의 반복 측정된 자료들이 독립이라고 가정한 모형을 주로 이용하였다. 본 연구에서는 기존 연구들에서 고려한 아동 학업성취도에 영향을 주는 변수들을 선택하여 반복 측정된 경시적 자료의 종속성을 고려한 고정효과와 임의효과를 포함하는 선형혼합모형으로 분석하여 아동 학업성취도에 영향을 주는 변수들은 무엇인지, 각 아동의 특성들이 반영되는 임의절편과 임의기울기가 있는지를 파악하는 것이 연구의 목적이다. 본 연구에 사용된 자료는 한국복지패널 1, 4, 7차 부가조사 중에서 아동용 설문문항에 대한 자료이고, 국어, 영어와 수학의 학업성취도 점수의 합을 아동 학업성취도로 한다. 선형혼합모형을 이용한 분석 시에 다중공선성의 검토와 결측치의 특성을 파악하고 적절한 오차의 상관행렬을 선택한다.

• 한국안전학회지
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• 제27권3호
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• pp.141-146
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• 2012

This study deals with the accident model using panel data which are composed of time series data of 2005 through 2007 and cross sectional data of link sections in Cheongju. Panel data are repeatedly collected over time from the same sample. The purpose of the study is to develop the traffic accident model using the above panel data. In pursuing the above, this study gives particular attentions to deriving the optimal models among various models including TSCSREG (Time Series Cross Section Regression). The main results are as follows. First, 8 panel data models which explained the various effects of accidents were developed. Second, $R^2$ values of fixed effect models were analyzed to be higher than those of random effect models. Finally, such the variables as the sum of the number of crosswalk on intersections and sum of the number of intersections were analyzed to be positive to the accidents.

• 문화기술의 융합
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• 제4권3호
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• pp.299-303
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• 2018

일반적으로 대공화기의 체계 명중률을 예측할 때 오차를 각각 고정편기, 가변편기 및 랜덤오차로 분류한 후 가변편기와 랜덤오차는 각 오차의 값의 제곱의 합의 제곱근으로 나타내고 고정편기의 경우는 오차의 합으로 나타낸다. 이때 각 오차의 단위 값의 변화에 관한 고각방향과 방위각 방향의 변위를 나타내는 변수가 가중치로 작용한다. 그리고 이 오차들을 이용하여 정규분포식의 적분을 통하여 체계 명중률을 예측한다. 본 논문에서는 오차의 상관관계를 고려하여 체계 명중률을 예측하는 방법을 제시한다. 본 접근법이 정밀한 체계 명중률을 예측하는데 도움이 된다는 것을 보인다.