• Journal of Korean Society of Industrial and Systems Engineering
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• v.35 no.2
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• pp.98-105
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• 2012

This paper describes the Bayesian approach for reliability demonstration test based on the samples from a finite population. The Bayesian approach involves the technical method about how to combine the prior distribution and the likelihood function to produce the posterior distribution. In this paper, the hypergeometric distribution is adopted as a likelihood function for a finite population. The conjugacy of the beta-binomial distribution and the hypergeometric distribution is shown and is used to make a decision about whether to accept or reject the finite population judging from a viewpoint of faulty goods. A numerical example is also given.

• Journal of the Korean Data and Information Science Society
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• v.23 no.3
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• pp.587-593
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• 2012

We study Bayesian estimates for finite population proportions in multinomial problems. To do this, we consider a three-stage hierarchical Bayesian model. For prior, we use Dirichlet density to model each cell probability in each cluster. Our method does not require complicated computation such as Metropolis-Hastings algorithm to draw samples from each density of parameters. We draw samples using Gibbs sampler with grid method. We apply this algorithm to a couple of simulation data under three scenarios and we estimate the finite population proportions using two kinds of approaches We compare results with the point estimates of finite population proportions and their standard deviations. Finally, we check the consistency of computation using differen samples drawn from distinct iterates.

• Communications for Statistical Applications and Methods
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• v.10 no.3
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• pp.647-654
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• 2003

Bayesian probability models for finite populations are considered assuming so-called the super-population. We find the posterior distribution of population mean by a new approach, using the concept of pivotal quantity for the small sample case. A large sample theory is also treated throught the concept of asymptotically pivotal quantity.

• Journal of the Korean Data and Information Science Society
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• v.17 no.4
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• pp.1309-1317
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• 2006

The paper considers some Bayes estimators of the finite population mean with auxiliary information under priors which are scale mixtures of normal, and thus have tail heavier than that of the normal. The proposed estimators are quite robust in general. Numerical methods of finding Bayes estimators under these heavy tailed priors are given, and are illustrated with an actual example.

• Journal of the Korean Data and Information Science Society
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• v.24 no.6
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• pp.1543-1550
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• 2013

In this paper, we study Bayesian estimation for the finite population proportion in binary data under selection bias. We use a Bayesian nonignorable selection model to accommodate the selection mechanism. We compare four possible estimators of the finite population proportions based on data analysis as well as Monte Carlo simulation. It turns out that nonignorable selection model might be useful for weekly biased samples.

• Journal of the Korean Statistical Society
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• v.27 no.3
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• pp.331-348
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• 1998

In this paper, we have proposed some robust Bayes estimators using ML-II priors as well as certain empirical Bayes estimators in estimating the finite population mean in the presence of auxiliary information. These estimators are compared with the classical ratio estimator and a subjective Bayes estimator utilizing the auxiliary information in terms of "posterior robustness" and "procedure robustness" Also, we have addressed the issue of choice of sampling design from a robust Bayesian viewpoint.

• Communications for Statistical Applications and Methods
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• v.22 no.3
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• pp.255-264
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• 2015

This paper addressed the problem of estimation of finite population mean in double sampling for stratification. This paper proposed a generalized ratio-cum-product type estimator of population mean. The bias and mean square error of the proposed estimator has been obtained upto the first degree of approximation. A particular member of the proposed generalized estimator was identified and studied from a comparison point of view. It is observed that the identified particular estimator is more efficient than usual unbiased estimator and Ige and Tripathi (1987) estimators. An empirical study was conducted in support of the theoretical findings.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.63-73
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• 1995

We consider some robust Bayes estimators using ML-II priors as well as certain empirical Bayes estimators in estimating the finite population mean. The proposed estimators are compared with the sample mean and subjective Bayes estimators in terms of "posterior robustness" and "procedure robustness".re robustness".uot;.

• Communications for Statistical Applications and Methods
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• v.15 no.5
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• pp.783-791
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• 2008

Estimation procedure of the finite population proportion and distribution function is considered. Based on a logistic regression model, an approximately model- optimal estimator is defined and conditions for the estimator to be design-consistent are given. Simulation study shows that the model-optimal design-consistent estimator defined under a logistic regression model performs well in estimating the finite population distribution function.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.3
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• pp.189-200
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• 2010

A numerical method is proposed and analyzed to approximate a mathematical model of age-dependent population dynamics with spatial diffusion. The model takes a form of nonlinear and nonlocal system of integro-differential equations. A finite difference method along the characteristic age-time direction is considered and primal mixed finite elements are used in the spatial variable. A priori error estimates are derived for the relevant variables.