• Journal of Korean Society for Quality Management
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• v.9 no.1
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• pp.3-11
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• 1981

A stress-strength model is formulated for s of k systems consisting of identical components. We consider minimum variance unbiased (MVU) estimation of system reliability for data consisting of a random sample from the stress distribution and one from the strength distribution when the two distirubtions are Weibull with unknown scale parameters and same known shape parameter. The asymptotic distribution of MVU estimate of system reliability in the model is obtained by using the standard asymptotic properties of the maximum likelihood estimate of system reliability and establishing their equivalence. Uniformly most accurate unbiased confidence intervals are also obtained for system reliability. Empirical comparison of the two estimates for small samples is studies by Monte Carlo simulation.

• Journal of Korean Society for Quality Management
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• v.18 no.2
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• pp.101-116
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• 1990

The objectives of this thesis are : first, to estimate the parameters and Pr[X < Y] in the Marshall and Olkin's Bivariate Exponential Distribution ; and secondly, to compare the Bayes estimators of Pr[X < Y] with maximum likelihood estimator of Pr[X < Y] in the Marshall and Olkin's Bivariate Exponential Distribution. Through the Monte Carlo Simulation, we observed that the Bayes estimators of Pr[X < Y] perform better than the maximum likelihood estimator of Pr[X < Y] and the Bayes estimator of Pr[X < Y] with gamma prior distribution performs better than with vague prior distribution with respect to bias and mean squared error in the Marshall and Olkin's Bivariate Exponential Distribution.

• International Journal of Reliability and Applications
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• v.6 no.2
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• pp.65-78
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• 2005

In this paper we derive estimations of the parameters included in the distribution of the lifetime of k-out-of-m cold standby system with imperfect switches. Maximum likelihood and Bayes procedures are followed to get such estimations. Numerical studies, using Monte Carlo simulation method, are given in order to explain how we can utilize the theoretical results derived, and to compare the performance of the two different methods used. The criterion of comparisons is the mean squared errors associated with each estimate.

• Communications for Statistical Applications and Methods
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• v.12 no.2
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• pp.285-294
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• 2005

This paper deals with the comparison of parameter estimation methods in a 3-parameter Kappa distribution which is sometimes used in flood frequency analysis. Method of moment estimation(MME), L-moment estimation(L-ME), and maximum likelihood estimation(MLE) are applied to estimate three parameters. The performance of these methods are compared by Monte-carlo simulations. Especially for computing MME and L-ME, three dimensional nonlinear equations are simplified to one dimensional equation which is calculated by the Newton-Raphson iteration under constraint. Based on the criterion of the mean squared error, L-ME (or MME) is recommended to use for small sample size( n$\le$100) while MLE is good for large sample size.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.35 no.3
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• pp.216-222
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• 2002

Autocorrelation in time series data can affect statistical inference in correlation or regression analyses. To improve a regression model from which the residuals are autocorrelated, Yule-Walker method, nonlinear least squares estimation, maximum likelihood method and 'prewhitening' method have been used to estimate the parameters in a regression equation. This study reviewed on the estimation methods of preventing spurious correlation in the presence of autocorrelation and applied the former three methods, Yule-Walker, nonlinear least squares and maximum likelihood method, to a 20-year real data set. Monte carlo simulation was used to compare the three parameter estimation methods. However, the simulation results showed that the mean squared error distributions from the three methods simulated do not differ significantly.

• Communications for Statistical Applications and Methods
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• v.24 no.5
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• pp.493-505
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• 2017

Maximum likelihood estimation (MLE) of the generalized extreme value distribution (GEVD) is known to sometimes over-estimate the positive value of the shape parameter for the small sample size. The maximum penalized likelihood estimation (MPLE) with Beta penalty function was proposed by some researchers to overcome this problem. But the determination of the hyperparameters (HP) in Beta penalty function is still an issue. This paper presents some data adaptive methods to select the HP of Beta penalty function in the MPLE framework. The idea is to let the data tell us what HP to use. For given data, the optimal HP is obtained from the minimum distance between the MLE and MPLE. A bootstrap-based method is also proposed. These methods are compared with existing approaches. The performance evaluation experiments for GEVD by Monte Carlo simulation show that the proposed methods work well for bias and mean squared error. The methods are applied to Blackstone river data and Korean heavy rainfall data to show better performance over MLE, the method of L-moments estimator, and existing MPLEs.

• Journal of The Korean Society of Agricultural Engineers
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• v.50 no.6
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• pp.37-47
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• 2008

Photovoltaic power generation is currently being recognized as one of the most popular sources for renewable resources over the country. Although it is also being adapted to rural area for may reasons, it is important to estimate the magnitudes of power outputs with reliable statistical methodologies, while applying historical daily solar energy data, for correct feasibility analysis. In this study, one of the well-known statistical methodologies is employed to define the appropriate probability distributions for monthly power outputs for the selected rural area, county of Seo-san, province of Chungnam. The results imply that the assumption of normal distributions for several months may lead to incorrect decision-making and therefore lead to the unreliable feasibility analysis. Generalized beta and triangular distributions were found to be superior to normal distribution, when describing monthly probability distributions for daily photovoltaic power. Based on the appropriate distributions resulted from this study, Monte Carlo simulation technique was also applied to provide additional flexible information for the relevant decision makers. This study found out new finding that the probability distributions should be considered to make planning of the photovoltaic power system in rural village unit, in order to give reasonable economic analysis to the decision makers.

• Communications for Statistical Applications and Methods
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• v.21 no.3
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• pp.213-224
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• 2014

In this paper, we study the problem of transforming to normality. We propose to estimate the transformation parameter by minimizing a weighted squared distance between the empirical characteristic function of transformed data and the characteristic function of the normal distribution. Our approach also allows for other symmetric target characteristic functions. Asymptotics are established for a random sample selected from an unknown distribution. The proofs show that the weight function $t^{-2}$ needs to be modified to have thinner tails. We also propose the method to compute the influence function for M-equation taking the form of U-statistics. The influence function calculations and a small Monte Carlo simulation show that our estimates are less sensitive to a few outliers than the maximum likelihood estimates.

• The Korean Journal of Applied Statistics
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• v.20 no.1
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• pp.79-89
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• 2007

A test for normality introduced by Arizono and Ohta(1989) is based on fullback-Leibler discrimination information. The test statistic is derived from the discrimination information estimated using sample entropy of Vasicek(1976) and the maximum likelihood estimator of the variance. However, these estimators are biased and so it is reasonable to make use of unbiased estimators to accurately estimate the discrimination information. In this paper, Arizono-Ohta test for normality is improved. The derived test statistic is based on the bias-corrected entropy estimator and the uniformly minimum variance unbiased estimator of the variance. The properties of the improved KL test are investigated and Monte Carlo simulation is performed for power comparison.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.47 no.10
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• pp.747-752
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• 2019

By using the failure information and the cumulative test execution time obtained by performing the reliability growth test, it is possible to estimate the parameter of the reliability growth model, and the Mean Time Between Failure (MTBF) of the product can be predicted through the parameter estimation. However the failure information could be acquired periodically or the number of sample data of the obtained failure information could be small. Because there are various constraints such as the cost and time of test or the characteristics of the product. This may cause the error of the parameter estimation of the reliability growth model to increase. In this study, the Bayesian method is applied to estimating the parameters of the reliability growth model when the number of sample data for the fault information is small. Simulation results show that the estimation accuracy of Bayesian method is more accurate than that of Maximum Likelihood Estimation (MLE) respectively in estimation the parameters of the reliability growth model.