• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.1
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• pp.55-72
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• 2009

A misclassified size-biased modified power series distribution (MSBMPSD) where some of the observations corresponding to x = c + 1 are misclassified as x = c with probability $\alpha$, is defined. We obtain its recurrence relations among the raw moments, the central moments and the factorial moments. Discussion of the effect of the misclassification on the variance is considered. To illustrate the situation under consideration some of its particular cases like the size-biased generalized negative binomial (SBGNB), the size-biased generalized Poisson (SBGP) and sizebiased Borel distributions are included. Finally, an example is presented for the size-biased generalized Poisson distribution to illustrate the results.

• Journal of the Korean Statistical Society
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• v.10
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• pp.97-104
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• 1981

It is shown that a lattice distribution defined on a set of n lattice points $L(n,\delta) = {\delta,\delta+1,...,\delta+n-1}$ is a distribution induced from the distribution of convolution of independently and identically distributed (i.i.d.) uniform [0,1] random variables. Also the m-th moment of the lattice distribution is obtained in a quite different approach from Park and Chung (1978). It is verified that the distribution of the sum of n i.i.d. uniform [0,1] random variables is completely determined by the lattice distribution on $L(n,\delta)$ and the uniform distribution on [0,1]. The factorial mement generating function, factorial moments, and moments are also obtained.

• East Asian mathematical journal
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• v.4
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• pp.175-182
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• 1988

• The Korean Journal of Applied Statistics
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• v.15 no.2
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• pp.395-403
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• 2002

In the third phase of the response surface methods, the first-order model is assumed and the curvature of the response surface is checked with a fractional factorial design augmented by centre runs. We further assume that a true model is a quadratic polynomial. To choose an optimal design, Box and Draper(1959) suggested the use of an average mean squared error (AMSE), an average of MSE of y(x) over the region of interest R. The AMSE can be partitioned into the average prediction variance (APV) and average squared bias (ASB). Since AMSE is a function of design moments, region moments and a standardized vector of parameters, it is not possible to select the design that minimizes AMSE. As a practical alternative, Box and Draper(1959) proposed minimum bias design which minimize ASB and showed that factorial design points are shrunk toward the origin for a minimum bias design. In this paper we propose a robust AMSE design which maximizes the minimum efficiency of the design with respect to a standardized vector of parameters.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.700-703
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• 2004

A reliability analysis and design procedure based on the design of experiment (DOE) is combined with the response surface method (RSM) for numerical efficiency. The procedure established is based on a 3$^n$ full factorial DOE for numerical quadrature using explicit formula of optimum levels and weights derived for general distributions. The full factorial moment method (FFMM) shows good performance in terms of accuracy and ability to treat non-normally distributed random variables. But, the FFMM becomes very inefficient because the number of function evaluation required increases exponentially as the number of random variables considered increases. To enhance the efficiency, the response surface moment method (RSMM) is proposed. In RSMM, experiments only with high probability are conducted and the rest of data are complemented by a quadratic response surface approximation without mixed terms. The response surface is updated by conducting experiments one by one until the value of failure probability is converged. It is calculated using the Pearson system and the four statistical moments obtained from the experimental data. A measure for checking the relative importance of an experimental point is proposed and named as influence index. During the update of response surface, mixed terms can be added into the formulation.

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1121-1148
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• 2017

Go is an ancient game of great complexity and has a huge following in East Asia. It is also very rich mathematically, and can be played on any graph, although it is usually played on a square lattice. As with any game, one of the most fundamental problems is to determine the number of legal positions, or the probability that a random position is legal. A random Go position is generated using a model previously studied by the author, with each vertex being independently Black, White or Uncoloured with probabilities q, q, 1 - 2q respectively. In this paper we consider the probability of legality for two scenarios. Firstly, for an $N{\times}N$ square lattice graph, we show that, with $q=cN^{-{\alpha}}$ and c and ${\alpha}$ constant, as $N{\rightarrow}{\infty}$ the limiting probability of legality is 0, exp($-2c^5$), and 1 according as ${\alpha}$ < 2/5, ${\alpha}=2/5$ and ${\alpha}$ > 2/5 respectively. On the way, we investigate the behaviour of the number of captured chains (or chromons). Secondly, for a random graph on n vertices with edge probability p generated according to the classical $Gilbert-Erd{\ddot{o}}s-R{\acute{e}}nyi$ model ${\mathcal{G}}$(n; p), we classify the main situations according to their asymptotic almost sure legality or illegality. Our results draw on a variety of probabilistic and enumerative methods including linearity of expectation, second moment method, factorial moments, polyomino enumeration, giant components in random graphs, and typicality of random structures. We conclude with suggestions for further work.

• The Journal of the Korea Contents Association
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• v.18 no.8
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• pp.300-314
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• 2018

This study, expending the existing concept of hostile media perception to biased media perception, empirically examined the effects of TV audience's political disposition(liberal, neutral, conservative) and broadcasting company's political disposition perceived by the audience(liberal, neutral, conservative) on evaluations of the broadcasting channel(interestedness, diversity, creativity, reliability, usefulness, fairness, public interest). With the nationwide online survey data from 624 adult audiences, a broadcasting company evaluated as the most neutral in political disposition at the moments of data gathering was selected and respondents' evaluations of the broadcasting channel were analyzed in a two-way factorial multiple analysis of covariance(MANCOVA). The results showed that the perceived political disposition of the broadcasting company affects audiences' evaluations of the channel while audiences' their own political dispositions do not. In addition, due to the interaction effects between audience's and broadcasting company's political dispositions, congruency in political dispositions led to positive evaluations(congenial media perceptions) while incongruency led to negative ones(hostile media perceptions). Based on these results, theoretical and empirical implications were discussed in terms of the formation of attitudes toward TV broadcasting channels.