• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.2
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• pp.157-160
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• 1999

We show the cumulants of a minimal sufficient statistics in k parameter natural exponential family by parameter function and partial parameter function. We nd the cumulants have some merits of central moments and general cumulants both. The first three cumulants are the central moments themselves and the fourth cumulant has the form related with kurtosis.

• Journal of the Korean Statistical Society
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• v.22 no.1
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• pp.55-69
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• 1993

Consider the problem of estimating an arbitrary continuous vector function under a weighted quadratic loss in the multiparameter exponential family with the density of the natural form. We first provide, using Blyth's (1951) method, a set of sufficient conditions for the admisibility of (possibly generalized Bayes) estimators and then treat some examples for normal, Poisson, and gamma distributions as applications of the main result.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.427-438
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• 2005

From a notion of d-pseudo-orthogonality for a sequence of poly-nomials ($d\;\in\;{2,3,\cdots}$), this paper introduces three different characterizations of natural exponential families (NEF's) with polynomial variance functions of exact degree 2d-1. These results provide extended versions of the Meixner (1934), Shanbhag (1972, 1979) and Feinsilver (1986) characterization results of quadratic NEF's based on classical orthogonal polynomials. Some news sets of polynomials with (2d-1)-term recurrence relation are then pointed out and we completely illustrate the cases associated to the families of positive stable distributions.

• Journal for History of Mathematics
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• v.9 no.2
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• pp.15-21
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• 1996

적률법(method of moment)이란 변수 X의 멱승에대한 기대치를 이용하여 분포의 성질을 알아보는 방법이다. 여기서 적률법이 이용되어진 역사적 배경을 소개하고, 3차 적률들의 선형적 성질을 비교하였다. 먼저, Kagan이 입증한 표본평균에 관한 3차 표본적률의 선형적 성질과 Bayesian 경우에 3차 사후적률(posterior moment)과 사후평균(posterior)의 선형성을 소개하였다. 그리고, 자연지수족(natural exponential family)아래서도 표본평균에 관한 3차 표본적률의 선형성을 알아보기 위해 단순함수(simple function)의 형태로 유도하였으며, 정규분포인 경우에 적용시켜 보았다.

• Journal of the Korean Data and Information Science Society
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• v.8 no.2
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• pp.247-260
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• 1997

The quasi-likelihood models which greatly widened the scope of generalized linear models are widely used in data analysis where a likelihood is not available. Since a quasi-likelihood may not appear to be an ordinary likelihood for any known distribution in the natural exponential family, to fit the quasi-likelihood models the standard statistical packages such as GLIM, GENSTAT, S-PLUS and so on may not directly applied. SAS/IML is very useful for fitting of such models. In this paper, we present simple SAS/IML(version 6.11) program which helps to fit and analyze the quasi-likelihood models applied to the leaf-blotch data introduced by Wedderburn(1974), and the problem with deviance useful generally to model checking is pointed out, and then its solution method is mention through the data analysis based on this quasi-likelihood models checking.

• Advances in Computational Design
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• v.7 no.1
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• pp.37-56
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• 2022

Phase-type distributions are the distributions of the time to absorption in finite and absorbing Markov chains. They generalize, while at the same time, retain the tractability of the exponential distributions and their family. They are widely used as stochastic models from queuing theory, reliability, dependability, and forecasting, to computer networks, security, and computational design. The ability to fit phase-type distributions to intractable or empirical distributions is, therefore, highly desirable for many practical purposes. Many methods and tools currently exist for this fitting problem. In this paper, we present the results of our investigation on using orthogonal-distance fitting as a method for fitting phase-type distributions, together with a comparison to the currently existing fitting methods and tools.