• Communications for Statistical Applications and Methods
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• 제5권3호
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• pp.733-742
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• 1998

For industrial and medical lifetime data, the generalized log-gamma regression model is considered. Then the Bayesian analysis for the generalized log-gamma regression with censored data are explained and following the data augmentation (Tanner and Wang; 1987), the censored data is replaced by simulated data. To overcome the complicated Bayesian computation, Makov Chain Monte Carlo (MCMC) method is employed. Then some modified algorithms are proposed to implement MCMC. Finally, one example is presented.

• 대한수학회논문집
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• 제15권1호
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• pp.45-50
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• 2000

The modified Hyers-Ulam-Rassias Stability Of the generalized form g(x+p) : $\phi$(x)g(x) for the Gamma functional equation shall be proved. As a consequence we obtain the stability theorems for the gamma functional equation.

• Journal of the Korean Statistical Society
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• 제36권1호
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• pp.93-109
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• 2007

Gamma distributions are some of the most popular models for hydrological processes. In this paper, a very flexible family which contains the gamma distribution as a particular case is introduced. Evidence of flexibility is shown by examining the shape of its pdf and the associated hazard rate function. A comprehensive treatment of the mathematical properties is provided by deriving expressions for the nth moment, moment generating function, characteristic function, Renyi entropy and the asymptotic distribution of the extreme order statistics. Estimation and simulation issues are also considered. Finally, a detailed application to drought data from the State of Nebraska is illustrated.

• 응용통계연구
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• 제31권4호
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• pp.475-484
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• 2018

감마 일반화 선형모형은 음이 아니며 치우침이 있는 반응변수에 유용한 모형으로 알려져 있다. 그러나 포아송 분포 또는 이항 분포에 기반한 일반화 선형모형에 비해 적은 관심을 받아왔다. 특히, 회귀계수의 유의성 검정에 대해서는 연구가 면밀히 되어 있지 않다. 본 논문에서는 감마 일반화 선형 모형의 검정에 대해 다양한 통계량들을 알아보고 수치 연구를 통해 그들의 성능을 비교한다. 수치 실험의 결과 부분 이탈도 검정 방법의 문제점이 나타났으며, 가능도비 검정 방법과 F-검정 방법이 좋은 성능을 보임을 확인하였다.

• 호남수학학술지
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• 제40권4호
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• pp.809-816
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• 2018

The aim of this research paper is to evaluate fifty double integrals invoving generalized hypergeometric function (25 each) in the form of $${{\int}^1_0}{{\int}^1_0}\;x^{{\gamma}-1}y^{{\gamma}+c-1}(1-x)^{c-1}(1-y)^{c+{\ell}}(1-xy)^{{\delta}-2c-{\ell}-1}{\times}_3F_2\[{^{a,\;b,\;2c+{\ell}+1}_{\frac{1}{2}(a+b+i+1),\;2c+j}}\;;{\frac{(1-x)y}{1-xy}}\]dxdy$$ and $${{\int}^1_0}{{\int}^1_0}\;x^{{\gamma}-1}y^{{\gamma}+c+{\ell}}(1-x)^{c+{\ell}}(1-y)^{c-1}(1-xy)^{{\delta}-2c-{\ell}-1}{\times}_3F_2\[{^{a,\;b,\;2c+{\ell}+1}_{\frac{1}{2}(a+b+i+1),\;2c+j}}\;;{\frac{1-y}{1-xy}}\]dxdy$$ in the most general form for any ${\ell}{\in}{\mathbb{Z}}$ and i, j = 0, ${\pm}1$, ${\pm}2$. The results are derived with the help of generalization of Edwards's well known double integral due to Kim, et al. and generalized classical Watson's summation theorem obtained earlier by Lavoie, et al. More than one hundred ineteresting special cases have also been obtained.

• 한국컴퓨터정보학회논문지
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• 제10권6호
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• pp.27-36
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• 2005

유한고장 속성을 가진 비동질적인 포아송 과정에 기초한 모형들에서 잔존 결함 1개당 고장 발생률은 일반적으로 상수, 흑은 단조증가 및 단조 감소 추세를 가지고 있다. 본 논문에서는 잔존 결함 1개당 고장 발생률이 단조증가(혹은, 단조감소) 속성을 가진 일반화 감마분포를 이용한 신뢰성 모형을 제안하였다. 일반화 감마분포를 이용한 유한 속성 비동질적 모형에 대한 모수추정은 고장 간격시간으로 구성된 실측자료를 이용하여 모수 추정을 수행하였다. 일반적 감마분포 형상모수의 제안을 위하여 특수한 형태를 적용하였다. 본 논문에서는 기존 모형의 분포를 적용하고 추가적인 소프트웨어 고장 해석을 위하여 감마 및 와이블 분포를 이용하였다. 일반화 감마 분포모형의 고장자료분석을 위하여 산술적 및 라플라스 검정, 적합도 검정, 편의 검정 등을 이용하였다.

• Asian-Australasian Journal of Animal Sciences
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• 제11권6호
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• pp.642-647
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• 1998

A Poisson error model as a generalized linear mixed model (GLMM) has been suggested for genetic analysis of counted observations. One of the assumptions in this model is the normality for random effects. Since this assumption is not always appropriate, a more flexible model is needed. For count traits, a Poisson hierarchical generalized linear model (HGLM) that does not require the normality for random effects was proposed. In this paper, a Poisson-Gamma HGLM was examined along with corresponding analytical methods. While a difficulty arises with Poisson GLMM in making inferences to the expected values of observations, it can be avoided with the Poisson-Gamma HGLM. A numerical example with simulated embryo yield data is presented.

• 대한수학회지
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• 제52권2호
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• pp.239-268
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• 2015

Let Q be a finite quiver and $G{\subseteq}Aut(\mathbb{k}Q)$ a finite abelian group. Assume that $\hat{Q}$ and ${\Gamma}$ are the generalized Mckay quiver and the valued graph corresponding to (Q, G) respectively. In this paper we discuss the relationship between indecomposable $\hat{Q}$-representations and the root system of Kac-Moody algebra $g({\Gamma})$. Moreover, we may lift G to $\bar{G}{\subseteq}Aut(g(\hat{Q}))$ such that $g({\Gamma})$ embeds into the fixed point algebra $g(\hat{Q})^{\bar{G}}$ and $g(\hat{Q})^{\bar{G}}$ as a $g({\Gamma})$-module is integrable.

• International Journal of Reliability and Applications
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• 제4권3호
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• pp.97-111
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• 2003

By applying Theorem 2.6.4 (Fang and Zhang, 1990, p.66) the dispersion matrix of a multivariate power exponential (MPE) distribution is derived. It is shown that the MPE and the gamma distributions are related and thus the MPE and chi-square distributions are related. By extending Fang and Xu's Theorem (1987) from the normal distribution to the Univariate Power Exponential (UPE) distribution an explicit expression is derived for calculating the probability of an UPE random variable over an interval. A representation of the characteristic function (c.f.) for an UPE distribution is given. Based on the MPE distribution the probability density functions of the generalized non-central chi-square, the generalized non-central t, and the generalized non-central F distributions are derived.

• 대한수학회논문집
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• 제20권1호
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• pp.93-106
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• 2005

In this paper, we obtain the generalization of the Hyers-Ulam-Rassias stability in the sense of Gavruta and Ger of the generalized G-type functional equations of the form $f({{\varphi}(x)) = {\Gamma}(x)f(x)$. As a consequence in the cases ${\varphi}(x) := x+p:= x+1$, we obtain the stability theorem of G-functional equation : the reciprocal functional equation of the double gamma function.