• Magazine of the Korean Society of Agricultural Engineers
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• v.39 no.3
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• pp.83-95
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• 1997

This study was conducted to derive optimal design floods by Gamma distribution models of the annual maximum series at eight watersheds along Geum , Yeong San and Seom Jin river Systems, Design floods obtained by different methods for evaluation of parameters and for plotting positions in the Gamma distribution models were compared by the relative mean errors and graphical fit along with 95% confidence interval plotted on Gamma probability paper. The results were analyzed and summarized as follows. 1.Adequacy for the analysis of flood flow data used in this study was confirmed by the tests of Independence, Homogeneity and detection of Outliers. 2.Basic statistics and parameters were calculated by Gamma distribution models using Methods of Moments and Maximum Likelihood. 3.It was found that design floods derived by the method of maximum likelihood and Hazen plotting position formular of two parameter Gamma distribution are much closer to those of the observed data in comparison with those obtained by other methods for parameters and for plotting positions from the viewpoint of relative mean errors. 4.Reliability of derived design floods by both maximum likelihood and method of moments with two parameter Gamma distribution was acknowledged within 95% confidence interval.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.115-120
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• 2003

Inference for probability P(Y

• Journal of the Korean Mathematical Society
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• v.33 no.1
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• pp.69-79
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• 1996

• Journal of the Korean Statistical Society
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• v.17 no.1
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• pp.46-55
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• 1988

Two-piece double exponential distribution (TPDE) with one piece $(X \leq 0)$ having the scale parameter $\theta_1$ while the other piece (X>0) having $\theta_2$ is considered here. Distribution of the sum of n-independent variables from such a distribution is obtained. Special cases of this distribution are also treated. Next, distribution of the ratio of two independent (TPDE) variables is derived. As an extension, distribution of $x_1/x_2x_3$ is expressed terms of hypergeometric functions. A small table gives the power of the test regarding double exponential against (TPDE).

• Journal of Navigation and Port Research
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• v.34 no.8
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• pp.609-614
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• 2010

This paper describes statistical parameter estimation to calculate collision probabilities between Mokpo Harbor Bridge and passing vessels. At first, we obtained AIS (Automatic Identification System) information from passing vessels, then after, analyzed the lateral distributions of vessel tracks and estimated the mean and the standard deviation for the distance away from bridge center, the passing course and the passing speed. The analysis results of track distribution for the distance away and the passing course are shown as normal type, otherwise the speed distribution shown as two kinds of different normal type. In addition, we testified that the usefulness of estimated parameter values through the relative comparison between the track distributions and it's normal probability distributions.

• The Korean Journal of Applied Statistics
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• v.26 no.3
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• pp.431-440
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• 2013

We consider the problem of estimating the parameters of heavy tailed distributions. In general, maximum likelihood estimation(MLE) is the most preferred method of parameter estimation because it has good properties such as asymptotic consistency, normality and efficiency. However, MLE is not always the best solution because MLE is unstable or does not exist in some cases. This paper proposes another parameter estimation method, non-linear least squares(NLS) and compares its performance to MLE. The NLS estimator is achieved by minimizing sum of squared difference between empirical cumulative distribution function(CDF) and a theoretical distribution function. In this article, we compare the NLS method to MLE using simulated data from heavy tailed distributions. The NLS method is shown to perform better than MLE in Burr distribution when the sample size is small; in addition, it performs well in a Frechet distribution.

• Journal of the Korea Institute of Military Science and Technology
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• v.14 no.1
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• pp.92-99
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• 2011

In this study, new multi-axial, critical plane based, fretting fatigue crack initiation parameter is developed by the addition of a new term into the Modified Shear Stress Range(MSSR) parameter. The newly developed parameter (MSSR') is then used to evaluate fretting fatigue life of titanium alloy, Ti-6A1-4V with various contact conditions. Finite element analysis is also used in order to obtain stress distribution on the contact surface during fretting fatigue test, which is then used for the calculation of fretting fatigue parameter. The MSSR' parameter shows better performance in predicting fretting fatigue lives from the conventional fatigue data, and less scattering within fretting fatigue data with different contact geometries.

• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.751-762
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• 2020

We define the average of a set of continuous functions of two variables (surfaces) using the structure of the two-parameter Wiener space that constitutes a probability space. The average of a sample set in the two-parameter Wiener space is defined employing the two-parameter Wiener process, which provides the concept of distribution over the two-parameter Wiener space. The average defined in our work, called an average function, also turns out to be a continuous function which is very desirable. It is proved that the average function also lies within the range of the sample set. The average function can be applied to model 3D shapes, which are regarded as their boundaries (surfaces), and serve as the average shape of them.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.30B no.12
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• pp.1-11
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• 1993

This paper concentrates on models useful for analyzing the error performance of ML(Maximum Likelihood) estimators of a single unknown signal parameter: that is the error intensity model. We first develop the point process representation for the estimation error and the conditional distribution of the estimator as well as the distribution of error candidate point process. Then the error intensity function is defined as the probability dessity of the estimate and the general form of the error intensity function is derived. We then develop several intensity models depending on the way we choose the candidate error locations. For each case, we compute the explicit form of the intensity function and discuss the trade-off among models as well as the extendability to the case of multiple parameter estimation.

• Journal of the Korean Statistical Society
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• v.28 no.4
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• pp.415-433
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• 1999

This paper considers the design of step-stress accelerated life tests for the Weibull distribution with a nonconstant shape parameter under Type I censoring. It is assumed that scale and shape parameters are log-linear functions of (possibly transformed) stress and that a cumulative exposure model holds for the effect of changing stress. The asymptotic variance of the maximum likelihood estimator of a stated quantile at design stress is used as an optimality criterion. The optimum three step-stress plans are presented for selected values of design parameters and the effects of errors in pre- estimates of the design parameters are investigated.