• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.14-14
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• 2003

Given a sequence ｛ $X_{n}$｝ of independent and identically distributed random variables with F, a sequential procedure for the p-th quantile ξ$_{P}$= $F^{-1}$ (P), 0$\beta$-protection. Some asymptotic properties for the proposed procedure and of an involved stopping time are proved: asymptotic consistency, asymptotic efficiency and asymptotic normality. From one of the results an effect of smoothing based on kernel functions is discussed. The results are also extended to the contaminated case.e.e.

• Journal of Korean Society for Quality Management
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• v.36 no.2
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• pp.20-27
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• 2008

Tolerance design has been identified as an important research area and a number of models have been proposed in the literature. This paper investigates the effect of limited capacity on tolerance design for products with nominal-the-best type (N-type) quality characteristics. The model is developed under the assumption that the reprocessed and nonreprocessed items are produced by the same manufacturing process and therefore their quality characteristics are identically and independently distributed. Profit models are constructed which involve four price/cost components; selling price, cost incurred by imperfect quality, reprocessing and quality inspection costs. Methods of finding the optimal tolerance limits are presented, and a numerical example is given. Sensitivity analyses are also performed to study the effect of a process standard deviation on this model.

• Communications for Statistical Applications and Methods
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• v.12 no.3
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• pp.557-587
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• 2005

This paper elucidates the limiting Gaussian distribution of a class of rank order statistics {$T_N$} for two sample problem pertaining to empirical processes of the squared residuals from two independent samples of GARCH processes. A distinctive feature is that, unlike the residuals of ARMA processes, the asymptotics of {$T_N$} depend on those of GARCH volatility estimators. Based on the asymptotics of {$T_N$}, we empirically assess the relative asymptotic efficiency and effect of the GARCH specification for some GARCH residual distributions. In contrast with the independent, identically distributed or ARMA settings, these studies illuminate some interesting features of GARCH residuals.

• Journal of the Korean Mathematical Society
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• v.46 no.4
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• pp.827-840
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• 2009

Let {$X_{ni}$ | $1{\leq}i{\leq}n,\;n{\geq}1$} be an array of rowwise negatively dependent (ND) random variables. We in this paper discuss the conditions of ${\sum}^n_{t=1}a_{ni}X_{ni}{\rightarrow}0$ completely as $n{\rightarrow}{\infty}$ under not necessarily identically distributed setting and the strong law of large numbers for weighted sums of arrays of rowwise negatively dependent random variables is also considered.

• Journal of the Korean Mathematical Society
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• v.51 no.1
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• pp.1-15
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• 2014

A conditional version of the classical central limit theorem is derived rigorously by using conditional characteristic functions, and a more general version of conditional central limit theorem for the case of conditionally independent but not necessarily conditionally identically distributed random variables is established. These are done anticipating that the field of conditional limit theory will prove to be of significant applicability.

• Communications for Statistical Applications and Methods
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• v.22 no.1
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• pp.69-80
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• 2015

In this paper, the probability that a given point is covered by a random convex hull generated by independent and identically-distributed random points in a plane is studied. It is shown that such probability can be expressed in terms of an integral that can be approximated numerically by function-evaluations over the grid-points in a 2-dimensional space. The new integral representation allows such probability be computed efficiently. The computational burdens under the proposed integral representation and those in the existing literature are compared. The proposed method is illustrated through numerical examples where the random points are drawn from (i) uniform distribution over a square and (ii) bivariate normal distribution over the two-dimensional Euclidean space. The applications of the proposed method in statistics are are discussed.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.515-521
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• 2010

In multivariate analysis, the inversion formula of the Stieltjes transform is used to find the density of a spectral distribution of random matrices of sample covariance type. Let $B_n\;=\;\frac{1}{N}Y_nY_n^TT_n$ where $Y_n\;=\;[Y_{ij}]_{n\;{\times}\;N}$ is with independent, identically distributed entries and $T_n$ is an $n\;{\times}\;n$ symmetric non-negative definite random matrix independent of the $Y_{ij}$'s. In the present paper, using the inversion formula of the Stieltjes transform, we will find that the limiting distribution of $B_n$ has a continuous density function away from zero.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2010.07a
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• pp.61-63
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• 2010

Recent work in compressed sensing theory shows that m${\times}$n independent and identically distributed sensing matrices whose entries are drawn independently from certain probability distributions guarantee exact recovery of a sparse signal with high probability even if m${\ll}$n. In particular, it is well understood that the L1 minimization algorithm is able to recover sparse signals from incomplete measurements. In this paper, we propose a novel sparse signal reconstruction method that is based on the reweighted L1 minimization via support recovery.

• Journal of the Korean Operations Research and Management Science Society
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• v.12 no.1
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• pp.27-33
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• 1987

A stochastic model for an inventory system in which depletion of stock takes place due to random demand as well as random loss of items is studied under the assumption that the intervals between cussessive unit demands as well as those between cussessive unit losses, are independently and identically distributed random variables having negative exponential distributions with respective parameters .mu. and .lambda. It is further assumed that leadtime for each order is an outstanding-order-dependent random variable. The steady state probability distribution of the net inventory level is derived under the continuous review (S -1, S) inventory policy, from which the total expected coast expression is formulated.

• Communications of the Korean Mathematical Society
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• v.16 no.2
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• pp.287-290
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• 2001

Let X$_1$, X$_2$, … be a sequence of independent and identically distributed random variables with continuous cumulative distribution function F(x). X(sub)j is an upper record value of this sequence if X(sub)j > max {X$_1$, X$_2$, …, X(sub)j-1}. We define u(n) = min {j│j > u(n-1), X(sub)j > X(sub)u(n-1), n $\geq$ 2} with u(1) = 1. Then F(x) = 1 - e(sup)-x/c, x > 0 if and only if E[X(sub)n(n+1) - X(sub)u(n)│X(sub)u(m) = y] = c or E[X(sub)u(n+2) - X(sub)u(n)│X(sub)u(m) = y] = 2c, n $\geq$ m+1.