• 물과 미래
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• 제7권2호
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• pp.99-106
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• 1974

The records of wave heights which were observed at Muk ho and Po hang of the East Coast of Korea were analized by several probility functions. The exponential 2 parameter distribution was found as the best fit probability function to the historical distribution of wave heights by the test of goodness of fit. But log-normal 2 parameter and log-extremal type A distributions were also fit to the historical distribution, especially in the Smirnov-Kolmogorov test. Therefore, it can't be always regarded that those two distributions are not fit to the wave heiht's distribution. In the test of goodness of fit, the Chi-Square test gave very sensitive results and Smirnov-Kolmogorov test, which is a distribution free and non-parametric test, gave more inclusive results. At the next stage, the inter-relationship between the mean and the one-third wave heights, the mean and the one-=tenth wave heights, the one-third and the one-tenth wave heights, the one-third and the highest wave heights were obtained and discussed.

• 전기학회논문지P
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• 제66권1호
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• pp.33-37
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• 2017

This paper describes the modeling of the failure rate estimation technique for applying the asset management technique to electric power facilities. There are many modeling techniques to estimate the failure rate. In this paper, the characteristics of the normal distribution, exponential distribution, weibull distribution, and piecewise linear functions are discussed. When evaluating reliability, the evaluation may be less meaningful if the sample data is insufficient. Therefore, Weibull distribution and piecewise linear function are adopted as the most suitable functions for estimating the failure rate of power facilities and the resulting failure rate function is derived.

• 자원환경지질
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• 제33권4호
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• pp.309-320
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• 2000

Aperture is an important parameter for determining the hydraulic characteristics of fractured media. In this study the topography of artificial rock joint surface was measured using 3D laser profilometer to analyze the aperture distribution. The initial aperture distribution was determined when the contact area became one percent of total joint surface. The initial aperture distribution of granite joint, with the mean value of 0.78 mm and the standard deviation of 0.34 mm was much different from that of the marble joint, with the mean value of 0.57 mm and the standard deviation of 0.26 mm. Apertures of both granite and marble showed normal distributions. Aperture distribution with the contact area of 25% was also analyzed. Mean value was decreased to one third compared to the initial aperture, but the standard deviation was decreased slightly. To determine the spatial correlation of the aperture distribution variogram analysis was carried out on the initial aperture data. Most experimental variograms were fitted well with exponential model. It is expected that the measured aperture characteristics can be used for stochastic analysis of fluid flow through rock joints.

• 대한수학회논문집
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• 제26권4호
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• pp.709-720
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• 2011

We obtain special type of differential equations which their solution are random variable with known continuous density function. Stochastic differential equations (SDE) of continuous distributions are determined by the Fokker-Planck theorem. We approximate solution of differential equation with numerical methods such as: the Euler-Maruyama and ten stages explicit Runge-Kutta method, and analysis error prediction statistically. Numerical results, show the performance of the Rung-Kutta method with respect to the Euler-Maruyama. The exponential two parameters, exponential, normal, uniform, beta, gamma and Parreto distributions are considered in this paper.

• 산업경영시스템학회지
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• 제20권41호
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• pp.157-166
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• 1997

Classical SPC charting methods such as (equation omitted), R, S charts assume high volume manufacturing processes where at least 25 or 30 calibrate samples of size 4 or 5 each can be gathered to estimate the process parameters before on-line charting actually begines. However, for many processes, especially in a job-shop setting, production runs are not necessarily long and charting technique are required that do not that depend upon knowing the process parameters in advance of the run. In this paper, using modifying statistics, we give a method for constructing control charts for the process mean when the measurements are from a normal distribution. In this case, consider that smaller weight being assigned to the older data as time process and properties and taking method of exponential smoothing constant$(\lambda)$ are suggested.

• Steel and Composite Structures
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• 제16권4호
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• pp.339-356
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• 2014

This paper presents a study of the nonlinear cylindrical bending of an exponential functionally graded plate (simply called E-FG) with variable thickness. The plate is subjected to uniform pressure loading and his geometric nonlinearity is introduced in the strain-displacement equations based on Von-Karman assumptions. The material properties of functionally graded plates, except the Poisson's ratio, are assumed to vary continuously through the thickness of the plate in accordance with the exponential law distribution; and the solution is obtained using Hamilton's principle for constant plate thickness. In order to analyze functionally graded plate with variable thickness, a numerical solution using finite difference method is used, where parabolic variation of the plate thickness is studied. The results for E-FG plates are given in dimensionless graphical forms; and the effects of material and geometric properties on displacements and normal stresses through the thickness are determined.

• Journal of the Korean Statistical Society
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• 제33권1호
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• pp.107-128
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• 2004

Bivariate Laplace distributions for which both marginal distributions and Laplace are discussed. Three kinds of bivariate Laplace distributions which are extended bivariate exponential distributions of Gumbel (1960) are introduced in this paper. These symmetrical distributions are compared with asymmetrical distributions of Kotz et al. (2000). Their probability density functions, cumulative distribution functions are derived. Conditional skewnesses and kurtoses are also defined. Their correlation coefficients are calculated and compared with others. We proposed bivariate random vector generating methods whose distributions are bivariate Laplace. With sample means and medians obtained from generated random vectors, variance and covariance matrices of means and medians are calculated and discussed with those of bivariate normal distribution.

• Communications for Statistical Applications and Methods
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• 제6권2호
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• pp.479-486
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• 1999

In this paper we propose the test statistic for ordered alternatives on multiple ranked set samples. Since the proposed test statistic is Page type its asymptotic properties are easily obtained. From the simulation works we calculate the power of test statistic($P_{RSS}$) under the underlying distributions such as uniform normal double exponential logistic and Cauchy distribution.

• Communications for Statistical Applications and Methods
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• 제16권3호
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• pp.449-461
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• 2009

최근의 생산 공정은 공정의 자동화, 고객 요구의 다양화 등으로 많은 품질 특성치들을 갖는 다변량 공정의 형태가 일반적이며, 벡터 공정능력지수는 이러한 다변량 공정의 능력을 평가하기 위한 대표적인 측도라 할 수 있다. 한편 공정의 분포에 대한 정보를 정확히 파악하기 어려운 실제 현장의 상황에서 보다 정확한 공정능력을 평가할 수 있는 통계적 추정 문제는 현실적으로 중요한 문제라고 할 수 있다. 본 논문에서는 특정한 이변량 지수 공정 하에서 이변량 벡터 공정능력지수 $C_{pkl}$에 대한 신뢰영역의 추정 문제에 관하여 연구하였다. 먼저 지수분포의 특성을 고려하여 실제 현장에서 널리 사용되고 있는 가장 기본적인 일변량 공정능력지수들 중에서 규격 하한만을 고려한 형태인 $C_{pkl}$에 관하여 이변량 벡터 공정능력지수 $C_{pkl}=(C_{pklx},\;C_{pkly})$로 확장 정의하고, 이 지수의 플러그-인 추정량 및 관련 극한 확률분포를 유도하였다. 또한 이 지수에 대해 Marshall과 Olkin (1967)의 이변량 지수분포 모형을 기초로 근사 신뢰영역을 제시하였으며, 모의실험을 통하여 이변량 벡터 공정능력지수 $C_{pkl}$에 대한 95% 정규 근사(Asymptotic Normality: AN) 신뢰영역에 대한 이용가능성 및 효율성을 비교 분석하였다.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2003년도 추계 학술발표회 논문집
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• pp.233-238
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• 2003

Goodness of fit test statistics based on the information discrepancy have been shown to perform very well (Vasicek 1976, Dudewicz and van der Meulen 1981, Chandra et al 1982, Gohkale 1983, Arizona and Ohta 1989, Ebrahimi et al 1992, etc). Although the test is well defined for the non-censored case, censored case has not been discussed in the literature. Therefore we consider a goodness of fit test based on the partial Kullback-Leibler(KL) information with the type II censored data. We derive the partial KL information of the null distribution function and a nonparametric distribution function, and establish a goodness of fit test statistic. We consider the exponential and normal distributions and made Monte Calro simulations to compare the test statistics with some existing tests.