• Journal of the Korean Mathematical Society
• /
• v.32 no.2
• /
• pp.321-328
• /
• 1995

Ibragimov(1975) showed the central limit theorem and the invariance principle for $\rho$-mixing random variables satisfying $\sigma^2(n) = nh(n) \longrightarrow \infty$ and $E$\mid$\zeta_0$\mid$^{2+\delta} < \infty$ for some $\delta > 0$ where $\sigma^2(n)$ denotes the variance of the partial sum $S_n$ and h(n) is a slowly varying function.

• Communications for Statistical Applications and Methods
• /
• v.16 no.4
• /
• pp.723-730
• /
• 2009

Missing values in time series can be treated as unknown parameters and estimated by maximum likelihood or as random variables and predicted by the expectation of the unknown values given the data. The purpose of this study is to impute missing values which are regarded as the maximum likelihood estimator and random variable in incomplete data and to compare with two methods using ARMA model. For illustration, the Mumps data reported from the national capital region monthly over the years 2001 ${\sim}$ 2006 are used, and results from two methods are compared with using SSF(Sum of square for forecasting error).

• ETRI Journal
• /
• v.35 no.4
• /
• pp.714-717
• /
• 2013

Peak power reduction techniques in orthogonal frequency division multiplexing (OFDM) has been an important subject for many researchers for over 20 years. In this letter, we propose a side-information-free technique that is based on the concept of random variable (RV) transformation. The suggested method transforms RVs into other RVs, aiming to reshape the constellation that will consequently produce OFDM symbols with a reduced peak-to-average power ratio. The proposed method has no limitation on the mapping type or the mapping order and has no significant effect on the bit error rate performance compared to other methods presented in the literature. Additionally, the computational complexity does not increase.

• Journal of the Korean Mathematical Society
• /
• v.54 no.6
• /
• pp.1879-1903
• /
• 2017

In this paper we study the closure property and probability tail asymptotics for randomly weighted sums $S^{\Theta}_n={\Theta}_1X_1+{\cdots}+{\Theta}_nX_n$ for long-tailed random variables $X_1,{\ldots},X_n$ and positive bounded random weights ${\Theta}_1,{\ldots},{\Theta}_n$ under similar dependence structure as in [26]. In particular, we study the case where the distribution of random vector ($X_1,{\ldots},X_n$) is generated by an absolutely continuous copula.

• The Journal of Natural Sciences
• /
• v.9 no.1
• /
• pp.57-60
• /
• 1997

Let {$X_{ni}$,1$\leq$i$\leq$,n$\geq$1} be an array of rowwise independent B-valued random variables which is uniformly bounded by a random various X satisfying $E|X|^{2p}<\infty$ for some p$\geq$1. Let {$a_{ni}$,1$\leq$i$\leq$,n$\geq$1} be an array of constants. Under some auxiliary conditions on {$a_{ni}$}, it is shown that $sum_{i=1}^n a_{ni}X_{ni}\rightarrow0$ in probability if and only if $sum_{i=1}^n a_{ni}X_{ni}$ converges completely ot 0.

• Journal of applied mathematics & informatics
• /
• v.27 no.1_2
• /
• pp.401-408
• /
• 2009

Let {$Y_i,-{\infty}<i<{\infty}$} be a doubly infinite sequence of identically distributed and ${\rho}^*$-mixing random variables and {$a_i,-{\infty}<i<{\infty}$} an absolutely summable sequence of real numbers. In this paper, we prove the complete convergence of $\{\sum\limits_{k=1}^n\;\sum\limits_{n=-\infty}^\infty\;a_{i+k}Y_i/n^{1/t};\;n{\geq}1\}$ under suitable conditions.

• Communications of the Korean Mathematical Society
• /
• v.20 no.3
• /
• pp.531-538
• /
• 2005

In this paper we derive the central limit theorem for ${\sum}_{i=1}^n\;a_{ni}\xi_i$, where ${a_{ni},\;1\;{\leq}\;i\;{\leq}\;n}$ is a triangular array of nonnegative numbers such that $sup_n{\sum}_{i=1}^n\;a_{ni}^2\;<\;{\infty},\;max_{1{\leq}i{\leq}n}a_{ni}{\rightarrow}0\;as\;n\;{\rightarrow}\;{\infty}\;and\;\xi'_i\;s$ are a linearly negative quadrant dependent sequence. We also apply this result to consider a central limit theorem for a partial sum of a generalized linear process $X_n\;=\;\sum_{j=-\infty}^\infty\;a_k+_j{\xi}_j$.

• Honam Mathematical Journal
• /
• v.34 no.2
• /
• pp.241-252
• /
• 2012

Let $\{X_{ni},\;1{\leq}i{\leq}n,\;n{\geq}1\}$ be a sequence of LNQD which are dominated randomly by another random variable X. We obtain the complete convergence and almost sure convergence of weighted sums ${\sum}^n_{i=1}a_{ni}X_{ni}$ for LNQD by using a new exponential inequality, where $\{a_{ni},\;1{\leq}i{\leq}n,\;n{\geq}1\}$ is an array of constants. As corollary, the results of some authors are extended from i.i.d. case to not necessarily identically LNQD case.

• Journal of the Korean Data and Information Science Society
• /
• v.17 no.3
• /
• pp.687-705
• /
• 2006

In this paper we consider GPH distribution that is defined as a distribution for sum of random number of random variables following exponential distribution. We establish approximation process of general distributions to GPH distributions and offer numerical results for various cases to show the accuracy of the approximation. We also propose analysis method of delay distribution of queueing systems using approximation to GPH distributions and offer numerical results for various queueing systems to show applicability of GPH approximation.

• Journal of the Chungcheong Mathematical Society
• /
• v.23 no.1
• /
• pp.127-136
• /
• 2010

For the maximum partial sum of linear process generated by a doubly infinite sequence of identically distributed $\rho$-mixing random variables with mean zeros, a complete convergence is obtained under suitable conditions.