• Communications for Statistical Applications and Methods
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• v.27 no.1
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• pp.47-64
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• 2020

In this paper, we derive some estimators of the scale parameter of the exponentiated half-logistic distribution based on the multiply Type-I hybrid censoring scheme. We assume that the shape parameter λ is known. We obtain the maximum likelihood estimator of the scale parameter σ. The scale parameter is estimated by approximating the given likelihood function using two different Taylor series expansions since the likelihood equation is not explicitly solved. We also obtain Bayes estimators using prior distribution. To obtain the Bayes estimators, we use the squared error loss function and general entropy loss function (shape parameter q = -0.5, 1.0). We also derive interval estimation such as the asymptotic confidence interval, the credible interval, and the highest posterior density interval. Finally, we compare the proposed estimators in the sense of the mean squared error through Monte Carlo simulation. The average length of 95% intervals and the corresponding coverage probability are also obtained.

• Journal of the Korean Society of Safety
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• v.10 no.2
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• pp.10-16
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• 1995

In estimating the fatigue data, only the uniform safety rate has been applied so far However, since more reasonable design concepts such as machine structures or subsidiary materials will be required in the future, the importance of a statistical estimation method for fatigue data is being highlighted. With such basic conception in mind, this study was aimed at critically discussing the interval estimation method which has been applied using the classical statistics thus far It was conceived that this conventional method would result in the estimation of the unstable side from the viewpoint of the likelihood Interval estimation method. In this regard, this study aimed at estimating the fatigue strength through the likelihood interval estimation method comparing it with the conventional interval estimation method would result in the estimation of the unstable side from the viewpoint of the likelihood interval estimation method. One of the methods using the likelihood for estimation data is the Bayes method. Based on this theory, statistical estimations were positivly applied, and thereupon, the fatigue data were estimated.

• Communications for Statistical Applications and Methods
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• v.13 no.1
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• pp.141-150
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• 2006

Penalized likelihood regression for exponential families have been considered by Kim (2005) through smoothing parameter selection and asymptotically efficient low dimensional approximations. We derive approximate Bayesian confidence intervals based on Bayes model associated with lower dimensional approximations to provide interval estimates in penalized likelihood regression and conduct empirical studies to access their properties.

• Journal of the Korean Data and Information Science Society
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• v.25 no.3
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• pp.643-653
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• 2014

In this paper, we propose some estimators for the extreme value distribution based on the interval method and mid-point approximation method from the progressive Type-I interval censored sample. Because log-likelihood function is a non-linear function, we use a Taylor series expansion to derive approximate likelihood equations. We compare the proposed estimators in terms of the mean squared error by using the Monte Carlo simulation.

• Communications for Statistical Applications and Methods
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• v.7 no.2
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• pp.481-487
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• 2000

When we construct an interval estimate of two independent proportions with rare events, the standard approach based on the normal approximation behaves badly in many cases. The problem becomes more severe when no success observations are observed on both groups. In this paper, we compare two alternative methods of constructing a confidence interval of the difference of two independent proportions by use of simulation. One is based on the profile likelihood and the other is the Bayesian probability interval. It is shown in this paper that the Bayesian interval estimator is easy to be implemented and performs almost identical to the best frequentist's method -the profile likelihood approach.

• Communications for Statistical Applications and Methods
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• v.17 no.3
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• pp.309-318
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• 2010

The construction of asymptotic confidence intervals is considered for the difference of binomial proportions in two doubly sampled data subject to false-positive error. The coverage behaviors of several likelihood based confidence intervals and a Bayesian confidence interval are examined. It is shown that a hierarchical Bayesian approach gives a confidence interval with good frequentist properties. Confidence interval based on the Rao score is also shown to have good performance in terms of coverage probability. However, the Wald confidence interval covers true value less often than nominal level.

• Communications for Statistical Applications and Methods
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• v.17 no.5
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• pp.679-688
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• 2010

Lee (2010) developed a confidence interval for the difference of binomial proportions in two doubly sampled data subject to false-positive errors. The confidence interval seems to be adequate for a general double sampling model subject to false-positive misclassification. However, in many applications, the false-positive error rates could be the same. On this note, the construction of asymptotic confidence interval is considered when the false-positive error rates are common. The coverage behaviors of nine likelihood based confidence intervals are examined. It is shown that the confidence interval based Rao score with the expected information has good performance in terms of coverage probability and expected width.

• Journal of the Korean Statistical Society
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• v.32 no.1
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• pp.1-10
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• 2003

We consider obtaining graphical summaries of uncertainty in estimates of parameters in nonlinear models. A nonlinear constrained optimization algorithm is developed for likelihood based confidence intervals for the functions of parameters in the model The results are applied to the problem of finding significance levels in nonlinear models.

• Journal of the Korean Data and Information Science Society
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• v.23 no.6
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• pp.1271-1277
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• 2012

In this paper, we propose an estimation method of the parameter in an exponential distribution based on a progressive Type I interval censored sample with semi-missing observation. The maximum likelihood estimator (MLE) of the parameter in the exponential distribution cannot be obtained explicitly because the intervals are not equal in length under the progressive Type I interval censored sample with semi-missing data. To obtain the MLE of the parameter for the sampling scheme, we propose a method by which progressive Type I interval censored sample with semi-missing data is converted to the progressive Type II interval censored sample. Consequently, the estimation procedures in the progressive Type II interval censored sample can be applied and we obtain the MLE of the parameter and survival function. It will be shown that the obtained estimators have good performance in terms of the mean square error (MSE) and mean integrated square error (MISE).

• Proceedings of the Korea Water Resources Association Conference
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• 2021.06a
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• pp.127-127
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• 2021

In order to estimate parameter uncertainty of hydrological models, the consideration of the likelihood functions which provide reliable parameters of model is necessary. In this study, the Bayesian Markov Chain Monte Carlo (MCMC) method with informal likelihood functions is used to analyze the uncertainty of parameters of the SURR model for estimating the hourly streamflow of Gunnam station of Imjin basin, Korea. Three events were used to calibrate and one event was used to validate the posterior distributions of parameters. Moreover, the performance of four informal likelihood functions (Nash-Sutcliffe efficiency, Normalized absolute error, Index of agreement, and Chiew-McMahon efficiency) on uncertainty of parameter is assessed. The indicators used to assess the uncertainty of the streamflow simulation were P-factor (percentage of observed streamflow included in the uncertainty interval) and R-factor (the average width of the uncertainty interval). The results showed that the sensitivities of parameters strongly depend on the likelihood functions and vary for different likelihood functions. The uncertainty bounds illustrated the slight differences from various likelihood functions. This study confirms the importance of the likelihood function selection in the application of Bayesian MCMC to the uncertainty assessment of the SURR model.