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

• 물과 미래
• /
• 제13권4호
• /
• pp.41-50
• /
• 1980

본 연구는 Gamma 분포의 이론적 검토와 이의 수공학에의 적용, 즉 Gamma 분포의 적합성 및 Gamma 모델에 의한 하천유량의 Simulation에 대한 연구와 검토를 행하는데 그 목적을 두고 있다. 분석에 있어서 우리나라 주요하천(낙동강, 한강 및 금강)의 월유량자료를 사용하였으며 분석을 간단하게 하기 위하여 자료를 Modular coefficient로 변환시켰다. 먼저 이변수 Gamma 분포형에 대한 월류량에의 적합성을 검정하였으며 이로부터 Gamma 분포형과 Monto Carlo 기법을 기초로 한 Gamma 모델에 의하여 월류량의 Simulation을 행하였다. 그 결과 기록치와 매우 근접한 Simulation 자료를 얻을 수 있었다.

• 한국산림과학회지
• /
• 제61권1호
• /
• pp.1-7
• /
• 1983

Weibull 분포함수(分布函數)에 의하여 임분(林分)의 직경(直徑) 분포(分布)를 추정(推定)할 수 있는 방법(方法) 중(中) 직경분포(直徑分布)의 실측치(實測値)로 직접(直接) 계산(計算)하는 방법(方法)에 대하여는 제(第) I 보(報)에서 발표(發表)하였다. 본(本) 연구(硏究)에서는 임의추출(任意抽出)한 표본목(標本木)의 평균직경(平均直徑)과 단면적평균직경(斷面績平均直徑)만을 구한 다음 Gamma함수(函數)를 사용(使用)한 Weibull 분포함수(分布函數)에 의하여 임분(林分)의 직경분포(直徑分布)를 추정(推定)하였다. 그 결과(結果) 실제(實際) 임분(林分)의 직경분포(直徑分布)와 매우 적합(適合)하였다. 그러므로 이 방법(方法)을 응용(應用)하면 임분(林分)의 직경분포(直徑分布)의 추정(推定)은 물론 장래(將來)의 임분구조(林分構造)의 해석(解析)과 예측(豫測)도 쉽게할 수 있다.

• Journal of the Korean Data and Information Science Society
• /
• 제15권4호
• /
• pp.753-758
• /
• 2004

A generalization of gamma distribution is defined by slightly modifying the form of Kobayashi's generalized gamma function(1991). We define a new extended gamma distribution and study some properties of this distribution.

• 한국화재소방학회논문지
• /
• 제30권2호
• /
• pp.62-67
• /
• 2016

본 연구에서는 워터 커튼용 노즐(Water curtian nozzle)의 액적 크기 분포(droplet size distribution)에 따라서 복사열을 감쇄하기 위한 광학 두께(optical depth)를 분석하였다. 액적 크기 분포를 측정하기 위해서 HELOS/VARIO 물 입자 측정 장치를 사용하였으며, Deirmenjian의 수정된 감마 분포 함수(modified gamma distribution function)를 적용하여 분사 특성을 정량화 하였다. 본 연구에서 사용한 워터 커튼용 노즐은 분포 상수(distribution constant) ${\alpha}=1$, ${\gamma}=5.2$의 값으로 나타났으며, 액적의 밀도 수(number density)를 고려한 분포 하중(droplet loading)과 액적 크기 분포 변화에 따라서 광학 두께에 관한 일반화된 관계식을 제시하였다. 본 연구 결과는 워터 커튼용 노즐의 설계 조건을 분석하기 위한 유용한 연구 자료가 될 것으로 사료된다.

• International Journal of Reliability and Applications
• /
• 제16권2호
• /
• pp.81-98
• /
• 2015

The Exponentiated Gamma (EG) distribution is one of the important families of distributions in lifetime tests. In this paper, a new generalized version of this distribution which is called kumaraswamy Exponentiated Gamma (KEG) distribution is introduced. A new distribution is more flexible and has some interesting properties. A comprehensive mathematical treatment of the KEG distribution is provided. We derive the $r^{th}$ moment and moment generating function of this distribution. Moreover, we discuss the maximum likelihood estimation of the distribution parameters. Finally, an application to real data sets is illustrated.

• 충청수학회지
• /
• 제22권1호
• /
• pp.1-5
• /
• 2009

Let {$X_n,\;n{\geq}1}$ be a sequence of independent identically distributed(i.i.d.) sequence of positive random variables with common absolutely continuous distribution function(cdf) F(x) and probability density function(pdf) f(x) and $E(X^2)<{\infty}$. The random variables $\frac{X_i{\cdot}X_j}{(\Sigma^n_{k=1}X_k)^{2}}$ and $\Sigma^n_{k=1}X_k$ are independent for $1{\leq}i if and only if {$X_n,\;n{\geq}1}$ have gamma distribution.

• 한국분말재료학회지
• /
• 제10권3호
• /
• pp.201-208
• /
• 2003

Distributions of diamond particles protruding on the surface of worn diamond segments in circular saw has been investigated. Scanning electron microscope was used to examine the worn ,surface and radial saw blade wear and grinding ratio was measured. The number of protruded diamond particle was approximately 50% of the total number of particles, and that was independent of diamond particle concentration and table speed. It was also noted that the inter-particle distance did not follow a symmetric function like Gaussian distribution function, instead it fitted well with a probability density function based on gamma function. The distribution of inter-particle spacing, therefore, was analyzed using a gamma function model.

• 충청수학회지
• /
• 제27권2호
• /
• pp.157-163
• /
• 2014

Let {$X_i$, $1{\leq}i{\leq}n$} be a sequence of i.i.d. sequence of positive random variables with common absolutely continuous cumulative distribution function F(x) and probability density function f(x) and $E(X^2)$ < ${\infty}$. The random variables X + Y and $\frac{(X-Y)^2}{(X+Y)^2}$ are independent if and only if X and Y have gamma distributions. In addition, the random variables $S_n$ and $\frac{\sum_{i=1}^{m}(X_i)^2}{(S_n)^2}$ with $S_n=\sum_{i=1}^{n}X_i$ are independent for $1{\leq}m$ < n if and only if $X_i$ has gamma distribution for $i=1,{\cdots},n$.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• 제15권12호
• /
• pp.4567-4583
• /
• 2021

This study proposes an analytical approximation algorithm based on extreme value theory (EVT) for the inverse of the power of the incomplete Gamma function. First, the Gumbel function is used to approximate the power of the incomplete Gamma function, and the corresponding inverse problem is transformed into the inversion of an exponential function. Then, using the tail equivalence theorem, the normalized coefficient of the general Weibull distribution function is employed to replace the normalized coefficient of the random variable following a Gamma distribution, and the approximate closed form solution is obtained. The effects of equation parameters on the algorithm performance are evaluated through simulation analysis under various conditions, and the performance of this algorithm is compared to those of the Newton iterative algorithm and other existing approximate analytical algorithms. The proposed algorithm exhibits good approximation performance under appropriate parameter settings. Finally, the performance of this method is evaluated by calculating the thresholds of space-time block coding and space-frequency block coding pattern recognition in multiple-input and multiple-output orthogonal frequency division multiplexing. The analytical approximation method can be applied to other related situations involving the maximum statistics of independent and identically distributed random variables following Gamma distributions.