• 충청수학회지
• /
• 제26권3호
• /
• pp.441-451
• /
• 2013

In this paper, we derive recurrence relations for moments of lower generalized order statistics within a class of doubly truncated distributions. Inverse Weibull, exponentiated Weibull, power function, exponentiated Pareto, exponentiated gamma, generalized exponential, exponentiated log-logistic, generalized inverse Weibull, extended type I generalized logistic, logistic and Gumble distributions are given as illustrative examples. Further, recurrence relations for moments of order statistics and lower record values are obtained as special cases of the lower generalized order statistics, also two theorems for characterizing the general form of distribution based on single moments of lower generalized order statistics are given.

• Water Engineering Research
• /
• 제2권1호
• /
• pp.1-10
• /
• 2001

The frequency analyses for the precipitation data in Korea were performed. We used daily maximum series, monthly maximum series, and annual series. For nonparametric frequency analyses, variable kernel estimators were used. Nonparametric methods do not require assumptions about the underlying populations from which the data are obtained. Therefore, they are better suited for multimodal distributions with the advantage of not requiring a distributional assumption. In order to compare their performance with parametric distributions, we considered several probability density functions. They are Gamma, Gumbel, Log-normal, Log-Pearson type III, Exponential, Generalized logistic, Generalized Pareto, and Wakeby distributions. The variable kernel estimates are comparable and are in the middle of the range of the parametric estimates. The variable kernel estimates show a very small probability in extrapolation beyond the largest observed data in the sample. However, the log-variable kernel estimates remedied these defects with the log-transformed data.

• 대한수학회보
• /
• 제59권4호
• /
• pp.979-991
• /
• 2022

A special class of exponential dispersion models is the class of Tweedie distributions. This class is very significant in statistical modeling as it includes a number of familiar distributions such as Gaussian, Gamma and compound Poisson. A Tweedie distribution has a power parameter p, a mean m and a dispersion parameter 𝜙. The value of the power parameter lies in identifying the corresponding distribution of the Tweedie family. The basic objective of this research work resides in investigating the existence of the implicit estimator of the power parameter of the Tweedie distribution. A necessary and sufficient condition on the mean parameter m, suggesting that the implicit estimator of the power parameter p exists, was established and we provided some asymptotic properties of this estimator.

• 한국농공학회지
• /
• 제21권4호
• /
• pp.108-117
• /
• 1979

In order to obtain the basic data for design of water structures which can be contributed to the planning of water use. Best fitted distribution function and the equations for the probable minimum flow were derived to the annual minimum flow of five subwatersheds along Geum River basin. The result were analyzed and summarized as follows. 1. Type III extremal distribution was considered as a best fit one among some other distributions such as exponential and two parameter lognormal distribution by $x^2$-goodness of fit test. 2. The minimum flow are analyzed by Type III extremal distribution which contains a shape parameter $\lambda$, a location parameter ${\beta}$ and a minimum drought $\gamma$. If a minimum drought $\gamma=0$, equations for the probable minimum flow, $D_T$, were derived as $D_T={\beta}e^{\lambda}1^{y'}$, with two parameters and as $D_T=\gamma+(\^{\beta}-\gamma)e^{{\lambda}y'}$ with three parameters in case of a minimum drought ${\gamma}>0$ respectively. 3. Probable minimum flow following the return periods for each stations were also obtained by above mentioned equations. Frequency curves for each station are drawn in the text. 4. Mathematical equation with three parameters is more suitable one than that of two parameters if much difference exist between the maximum and the minimum value among observed data.

• 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.

• Journal of the Korean Statistical Society
• /
• 제20권1호
• /
• pp.57-66
• /
• 1991

This paper deals with the problem of estimating an arbitrary piecewise continuous function of the parameter under squared error loss in the one parameter exponential family. Using Blyth's(1951) method sufficient conditions are given for the admissibility of (possibly generalized Bayes) estimators. Also, some examples are provided for normal, binomial, and gamma distributions.

• 한국방사성폐기물학회:학술대회논문집
• /
• 한국방사성폐기물학회 2005년도 추계 학술대회 논문집
• /
• pp.296-297
• /
• 2005

• 한국방사성폐기물학회:학술대회논문집
• /
• 한국방사성폐기물학회 2018년도 추계학술논문요약집
• /
• pp.345-346
• /
• 2018

• 한국방사성폐기물학회:학술대회논문집
• /
• 한국방사성폐기물학회 2018년도 춘계학술논문요약집
• /
• pp.401-402
• /
• 2018

• 한국방사선학회논문지
• /
• 제11권6호
• /
• pp.509-515
• /
• 2017

본 연구는 EBT3 필름을 이용하여 감마나이프 퍼펙션 모델의 3차원적인 선량분포 측정하고 기준값과 비교 분석하여 표준화된 측정방법의 기초로 활용하고자 한다. 2개 종합병원에 설치된 감마나이프 퍼펙션 모델의 선량 분포를 EBT3 필름을 이용하여 정확도와 정밀도를 평가하였다. 정확도 평가를 위해 4 mm 콜리메터를 사용하여 기계적인 중심축과 선량중심축의 일치도를 측정하였다. A병원 0.098 mm, 0.195 mm 이며 B 병원 0.229 mm, 0.223 mm 로 허용 오차 0.3 mm 이하로 측정되었다. 정밀도 평가는 4, 8, 16 mm 콜리메터(collimater) 각각의 x, y, z 3차원면 에서의 반치폭(FWHM : Full Width at Half Maximum)을 이미지-제이 프로그램을 이용하여 평가하였다. A 병원은 -0.283~0.583 mm, B 병원은 -0.857~0.810 mm로 50%선 ${\pm}1mm$ 이하의 기준에 적합하였다. 이미지-제이 프로그램을 이용한 선량 분포 분석의 경우 측정자 간의 오차가 발생 가능함으로 측정점에 대한 명확한 기준을 확립할 필요가 있으며, 감마나이프 방사선 수술이 시행되어지는 고선량 영역에서 사용 가능한 선량영역이 높은 필름을 이용한 치료계획과 실제 치료 조사면의 비교가 필요하다고 생각된다.