• Journal of the Korean Data and Information Science Society
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• v.15 no.4
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• pp.743-752
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• 2004

In this paper, we develop the Bayesian model selection procedure using the reference prior for comparing two nested model such as the independent and intraclass models using the distance or divergence between the two as the basis of comparison. A suitable criterion for this is the power divergence measure as introduced by Cressie and Read(1984). Such a measure includes the Kullback -Liebler divergence measures and the Hellinger divergence measure as special cases. For this problem, the power divergence measure turns out to be a function solely of $\rho$, the intraclass correlation coefficient. Also, this function is convex, and the minimum is attained at $\rho=0$. We use reference prior for $\rho$. Due to the duality between hypothesis tests and set estimation, the hypothesis testing problem can also be solved by solving a corresponding set estimation problem. The present paper develops Bayesian method based on the Kullback-Liebler and Hellinger divergence measures, rejecting $H_0:\rho=0$ when the specified divergence measure exceeds some number d. This number d is so chosen that the resulting credible interval for the divergence measure has specified coverage probability $1-{\alpha}$. The length of such an interval is compared with the equal two-tailed credible interval and the HPD credible interval for $\rho$ with the same coverage probability which can also be inverted into acceptance regions of $H_0:\rho=0$. Example is considered where the HPD interval based on the one-at- a-time reference prior turns out to be the shortest credible interval having the same coverage probability.

• 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.

• Proceedings of the Korean Institute Of Construction Engineering and Management
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• autumn
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• pp.478-481
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• 2002

In these days, Cost and Scheduling was managed effectively because of introduction of EVMS to construction project. However the EVMS is appropriate methods to advanced country, so it is difficult to apply into domestic construction project. in this paper weighted value n, m was used of compositive index(CI) to forecast Estimate At Completion (EAC) using statistical analysis in credible interval the objective of this paper is to verify compositive index(CI) and to forecast Estimate At Completion (EAC).

• Journal of the Korean Statistical Society
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• v.27 no.4
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• pp.421-433
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• 1998

In this paper, matching priors for P(X < Y) are investigated when both distributions are exponential distributions. Two recent approaches for finding noninformative priors are introduced. The first one is the verger and Bernardo's forward and backward reference priors that maximizes the expected Kullback-Liebler Divergence between posterior and prior density. The second one is the matching prior identified by matching the one sided posterior credible interval with the frequentist's desired confidence level. The general forms of the second- order matching prior are presented so that the one sided posterior credible intervals agree with the frequentist's desired confidence levels up to O(n$^{-1}$ ). The frequentist coverage probabilities of confidence sets based on several noninformative priors are compared for small sample sizes via the Monte-Carlo simulation.

• Journal of the Korean Data and Information Science Society
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• v.24 no.6
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• pp.1455-1464
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• 2013

This paper develops maximum likelihood estimators (MLEs) of unknown parameters in an exponentiated half-logistic distribution based on a progressively type-II censored sample. We obtain approximate confidence intervals for the MLEs by using asymptotic variance and covariance matrices. Using importance sampling, we obtain Bayes estimators and corresponding credible intervals with the highest posterior density and Bayes predictive intervals for unknown parameters based on progressively type-II censored data from an exponentiated half logistic distribution. For illustration purposes, we examine the validity of the proposed estimation method by using real and simulated data.

• Proceedings of the Korea Society for Industrial Systems Conference
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• 1999.05a
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• pp.191-197
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• 1999

In this paper, we develop noninformative priors that are used for estimating the reliability of stress-strength system under the Burr-type X distribution. A class of priors is found by matching the coverage probabilities of one-sided Bayesian credible interval with the corresponding frequentist coverage probabilities. It turns out that the reference prior is a first order matching prior. The propriety of posterior under matching prior is provided. The frequentist coverage probabilities are given for small samples.

• Communications for Statistical Applications and Methods
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• v.13 no.1
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• pp.89-99
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• 2006

This article deals with the problem of estimating parameters of Burr Type XII distribution, on the basis of a general progressive Type II censored sample using Bayesian viewpoints. The maximum likelihood estimator does not admit closed form but explicit sharp lower and upper bounds are provided. Assuming squared error loss and linex loss functions, Bayes estimators of the parameter k, the reliability function, and the failure rate function are obtained in closed form. Finally, a simulation study is also included.

• Proceedings of the Korean Association for Survey Research Conference
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• 2006.06a
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• pp.131-159
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• 2006

This paper consider multinomial group testing which is concerned with classification each of N given units into one of k disjoint categories. In this paper, we propose exact Bayesian, approximate Bayesian, bootstrap methods for estimating individual category proportions using the multinomial group testing model proposed by Bar-Lev et al (2005). By the comparison of Mcan Squre Error (MSE), it is shown that the exact Bayesian method has a bettor efficiency and consistency than maximum likelihood method. We suggest an approximate Bayesian approach using Markov Chain Monte Carlo (MCMC) for posterior computation. We derive exact credible intervals based on the exact Bayesian estimators and present confidence intervals using the bootstrap and MCMC. These intervals arc shown to often have better coverage properties and similar mean lengths to maximum likelihood method already available. Furthermore the proposed models are illustrated using data from a HIV blooding test study throughout California, 2000.

• Journal of the Korean Statistical Society
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• v.29 no.1
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• pp.17-27
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• 2000

In this paper, we develop noninformative priors that are used for estimating the reliability of stress-strength system under the Burr-type X model. A class of priors is found by matching the coverage probabilities of one-sided Bayesian credible interval with the corresponding frequentist coverage probabilities. It turns out that the reference prior as well as the Jeffreys prior are the second order matching prior. The propriety of posterior under the noninformative priors is proved. The frequentist coverage probabilities are investigated for samll samples via simulation study.

• Journal of the Korean Data and Information Science Society
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• v.13 no.2
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• pp.235-242
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• 2002

In this paper, we develop noninformative priors that are used for estimating the ratio of failure rates under Freund's bivariate exponential distribution. A class of priors is found by matching the coverage probabilities of one-sided Baysian credible interval with the corresponding frequentist coverage probabilities. Also the propriety of posterior under the noninformative priors is proved and the frequentist coverage probabilities are investigated for small samples via simulation study.