• 한국수학교육학회지시리즈B:순수및응용수학
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• 제8권2호
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• pp.79-85
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• 2001

As most Of distributions in applications have a finite support, we introduce the class of finite distributions with the known shape of their central part and the unknown tails. Furthermore, we use the Huber minimax approach to determine the unknown characteristics of this class. We obtain the least informative distributions minimizing Fisher information for location in the classes of the truncated Gaussian and uniform distributions, and these results give the reasonable values of the thresholds of truncation. The properties of the obtained solutions are discussed.

• Communications for Statistical Applications and Methods
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• 제26권1호
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• pp.57-67
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• 2019

Income distribution is a major concern in economic theory. In regional economics, it is often of interest to compare income distributions in different regions. Traditional methods often compare the income inequality of different regions by assuming parametric forms of the income distributions, or using summary statistics like the Gini coefficient. In this paper, we propose a nonparametric procedure to test for heterogeneity in income distributions among different regions, and a K-means clustering procedure for clustering income distributions based on energy distance. In simulation studies, it is shown that the energy distance based method has competitive results with other common methods in hypothesis testing, and the energy distance based clustering method performs well in the clustering problem. The proposed approaches are applied in analyzing data from China Health and Nutrition Survey 2011. The results indicate that there are significant differences among income distributions of the 12 provinces in the dataset. After applying a 4-means clustering algorithm, we obtained the clustering results of the income distributions in the 12 provinces.

• 대한수학회논문집
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• 제13권3호
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• pp.629-634
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• 1998

As most of distributions appearing in applications are finite but with the unknown domain of finiteness, we propose to use the robust minimax approach for the determination of the boundaries of this domain. The obtained least favorable distribution minimizing Fisher information over the class of the approximately Gaussian finite distributions gives the reasonable sizes of the domain of finiteness and the thresholds of truncation.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1998년도 The Third Asian Fuzzy Systems Symposium
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• pp.659-662
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• 1998

In this paper, lower and upper possibility distributions are identified to reflect two extreme opinions in portfolio selection problems based on upper and lower possibility distributions are formalized as quadratic programming problems. Portfolios for compromising two extreme opinions from upper and lower possibility distributions and balancing the opinions of a group of experts can be obtained by quadratic optimization problems, respectively.

• Journal of the Korean Data and Information Science Society
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• 제22권3호
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• pp.505-513
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• 2011

본 논문의 목적은 후진 미분 연산자를 이용하여 이산확률분포에 대한 원점으로부터의 r차 적률을 구하는 공식을 유도한다. 이 공식을 이용함으로써 r차 적률은 0에서 계산된 $x^r$의 r번째 후진 미분 연산자까지의 일차결합으로써 계산됨을 알 수 있다.

• 대한수학회논문집
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• 제23권2호
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• pp.201-209
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• 2008

In this paper we introduce two products of tempered distributions with positive support. These products are based in the Laguerre representation of distributions. We calculate some products as, $[{\delta}]x^{\lambda}_+={\delta}[x^{\lambda}_+]=0\;and\;[x^{\lambda}_+]x^{\mu}_+=x^{{\lambda}+{\mu}}_+$ for appropriate ${\lambda}$ and ${\mu}$.

• Journal of applied mathematics & informatics
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• 제40권5_6호
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• pp.925-931
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• 2022

In this article, we compare the reliability and the hazard function between a baseline distribution and the corresponding transmuted-G distribution. Some examples based on existing transmuted-G distributions in literature are used. Three tests of parameter significance are utilized to test the importance of a transmuted-G distribution over the baseline distribution, and real data is used in an application of the inference about the importance of transmuted-G distributions.

• Journal of the Korean Statistical Society
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• 제36권3호
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• pp.349-355
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• 2007

In this paper we study some important properties of the bivariate generalized hypergeometric probability (BGHP) distribution by establishing the existence of all the moments of the distribution and by deriving recurrence relations for raw moments. It is shown that certain mixtures of BGHP distributions are again BGHP distributions and a limiting case of the distribution is considered.

• Journal of the Korean Statistical Society
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• 제34권1호
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• pp.35-38
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• 2005

A single, tractable, special case of the problem of continuous mixtures of beta distributions over their parameters is considered. This is the uniform mixture of generalized arc-sine distributions which, curiously, turns out to be linked by transformation to the Cauchy distribution.

• 호남수학학술지
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• 제27권3호
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• pp.421-429
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• 2005

Generalizing the results in [7] that considers several functional equations in the spaces of the Schwartz tempered distributions and the Fourier hyperfunctions we consider Pexider type functional equations in the space of distributions.