• Bulletin of the Korean Chemical Society
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• v.13 no.6
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• pp.665-669
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• 1992

We consider the problem of a random walker on a one-dimensional lattice (N sites) confronting a centrally-located deep trap (trapping probability, T=1) and N-1 adjacent sites at each of which there is a nonzero probability s(0 < s < 1) of the walker being trapped. Exact analytic expressions for < n > and the average number of steps required for trapping for arbitrary s are obtained for two types of finite boundary conditions (confining and reflecting) and for the infinite periodic chain. For the latter case of boundary condition, Montroll's exact result is recovered when s is set to zero.

• Journal of the Korean Statistical Society
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• v.28 no.2
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• pp.225-234
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• 1999

We consider the following semi-parametric non-linear mixed effect regression model : y\ulcorner=f($\chi$\ulcorner;$\beta$)+$\sigma$$\mu$($\chi$\ulcorner)+$\sigma$$\varepsilon$\ulcorner,i=1,…,n,y*=f($\chi$;$\beta$)+$\sigma$$\mu$($\chi$) where y'=(y\ulcorner,…,y\ulcorner) is a vector of n observations, y* is an unobserved new random variable of interest, f($\chi$;$\beta$) represents fixed effect of known functional form containing unknown parameter vector $\beta$\ulcorner=($\beta$$_1$,…,$\beta$\ulcorner), $\mu$($\chi$) is a random function of mean zero and the known covariance function r(.,.), $\varepsilon$'=($\varepsilon$$_1$,…,$\varepsilon$\ulcorner) is the set of uncorrelated measurement errors with zero mean and unit variance and $\sigma$ is an unknown dispersion(scale) parameter. On the basis of finite-sample, small-dispersion asymptotic framework, we derive an absolute lower bound for the asymptotic mean squared errors of prediction(AMSEP) of the regular-consistent non-linear predictors of the new random variable of interest y*. Then we construct an optimal predictor of y* which attains the lower bound irrespective of types of distributions of random effect $\mu$(.) and measurement errors $\varepsilon$.

• Smart Structures and Systems
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• v.10 no.2
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• pp.89-110
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• 2012

This study was intended to efficiently perform the probabilistic optimal safety assessment of steel cable-stayed bridges (SCS bridges) using stochastic finite element analysis (SFEA) and expected life-cycle cost (LCC) concept. To that end, advanced probabilistic finite element algorithm (APFEA) which enables to execute the static and dynamic SFEA considering aleatory uncertainties contained in random variable was developed. APFEA is the useful analytical means enabling to conduct the reliability assessment (RA) in a systematic way by considering the result of SFEA based on linearity and nonlinearity of before or after introducing initial tensile force. The appropriateness of APFEA was verified in such a way of comparing the result of SFEA and that of Monte Carlo Simulation (MCS). The probabilistic method was set taking into account of analytical parameters. The dynamic response characteristic by probabilistic method was evaluated using ASFEA, and RA was carried out using analysis results, thereby quantitatively calculating the probabilistic safety. The optimal design was determined based on the expected LCC according to the results of SFEA and RA of alternative designs. Moreover, given the potential epistemic uncertainty contained in safety index, failure probability and minimum LCC, the sensitivity analysis was conducted and as a result, a critical distribution phase was illustrated using a cumulative-percentile.

• Communications for Statistical Applications and Methods
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• v.9 no.3
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• pp.765-774
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• 2002

Suppose one is given a vector X of a finite set of quantities $X_i$ which are independent Poisson random variables. A null hypothesis $H_0$ about E(X) is to be tested against an alternative hypothesis $H_1$. A quantity $\sum\limits_{i}w_ix_i$ is to be computed and used for the test. The optimal values of $W_i$ are calculated for three cases: (1) signal to noise ratio is used in the test, (2) normal approximations with unequal variances to the Poisson distributions are used in the test, and (3) the Poisson distribution itself is used. The above three cases are considered to the situations that are without background noise and with background noise. A comparison is made of the optimal values of $W_i$ in the three cases for both situations.

• Journal of Communications and Networks
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• v.5 no.2
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• pp.96-103
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• 2003

Asymptotic theorems are very commonly used in probability. For systems whose performance depends on a set of n random parameters, asymptotic analyses for n${\to}{\infty}$ are often used to simplify calculations and obtain results yielding useful hints at the behavior of the system for finite n. These asymptotic analyses are especially useful whenever the convergence to the asymptotic results is so fast that even for moderate n they yield results close to the true values. This tutorial paper illustrates this principle by applying it to capacity calculations of multiple-antenna systems.

• Communications for Statistical Applications and Methods
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• v.16 no.5
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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.

• Communications for Statistical Applications and Methods
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• v.22 no.2
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• pp.137-146
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• 2015

Singh (2013) considered the dual problem to the calibration of design weights to obtain a new generalized linear regression estimator (GREG) for the finite population total. In this work, we have made an attempt to suggest a way to use the dual calibration of the design weights in case of multi-auxiliary variables; in other words, we have made an attempt to give an answer to the concern in Remark 2 of Singh (2013) work. The same idea is also used to generalize the GREG estimator proposed by Deville and S$\ddot{a}$rndal (1992). It is not an easy task to find the optimum values of the parameters appear in our approach; therefore, few suggestions are mentioned to select values for such parameters based on a random sample. Based on real data set and under simple random sampling without replacement design, our approach is compared with other approaches mentioned in this paper and for different sample sizes. Simulation results show that all estimators have negligible relative bias, and the multivariate case of Singh (2013) estimator is more efficient than other estimators.

• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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• pp.305-314
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• 1999

The Hsu-Robbins-erd s theorem states that if {$X_m,n\geq1$} is a sequence of independent and identically distributed random variables, then ${EX_1}^2<\infty$ and $EX_1$=0 if and only if ${\sum_{n=1}}^\infty\;P($\mid${\sum_{k=1}}^nX_k$\mid$\geqn\in)<\infty$ for every $\in$ > 0. Under some auxiliary conditions, Sp taru (1994) extended this to the case where the $X_n$ are independent, but their distributions come from a finite set. Pruss (1996) proved Sp taru's result under weaker conditions, The purpose of this paper is to improve Pruss conditions.

• The Korean Journal of Applied Statistics
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• v.30 no.1
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• pp.57-68
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• 2017

Clustering algorithms attempt to find a partition of a finite set of objects in to a potentially predetermined number of nonempty subsets. Gibbs sampling of a normal mixture of linear mixed regressions with a Dirichlet prior distribution calculates posterior probabilities when the number of clusters was known. Our approach provides simultaneous partitioning and parameter estimation with the computation of classification probabilities. A Monte Carlo study of curve estimation results showed that the model was useful for function estimation. Examples are given to show how these models perform on real data.

• Proceedings of the IEEK Conference
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• 1998.06a
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• pp.106-109
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• 1998

Wireless communication systems, in particular, must operate in a crowded electro-magnetic environmnet where in-band undesired signals are treated as noise by the receiver. These interfering signals are often random but not Gaussian Due to nongaussian noise, the distribution of the observables cannot be specified by a finite set of parameters; instead r-dimensioal sample space (pure noise samples) is equiprobably partitioned into a finite number of disjointed regions using quantiles and a vector quantizer based on training samples. If we assume that the detected symbols are correct, then we can observe the pure noise samples during the training and transmitting mode. The algorithm proposed is based on a piecewise approximation to a regression function based on quantities and conditional partition moments which are estimated by a RMSA (Robbins-Monro Stochastic Approximation) algorithm. In this paper, we develop a diversity combiner with modified detector, called Non-Linear Detector, and the receiver has a differential phase detector in each diversity branch and at the combiner each detector output is proportional to the second power of the envelope of branches. Monte-Carlo simulations were used as means of generating the system performance.