• Journal of the Korean Data and Information Science Society
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• v.27 no.4
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• pp.1091-1100
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• 2016

This paper considers the noninformative priors for the linear function of parameters in the lognormal distribution. The lognormal distribution is applied in the various areas, such as occupational health research, environmental science, monetary units, etc. The linear function of parameters in the lognormal distribution includes the expectation, median and mode of the lognormal distribution. Thus we derive the probability matching priors and the reference priors for the linear function of parameters. Then we reveal that the derived reference priors do not satisfy a first order matching criterion. Under the general priors including the derived noninformative priors, we check the proper condition of the posterior distribution. Some numerical study under the developed priors is performed and real examples are illustrated.

• 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.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.709-723
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• 2024

We study the distributions of waiting times in variations of the geometric distribution of order k. Variation imposes length on the runs of successes and failures. We study two types of waiting time random variables. First, we consider the waiting time for a run of k consecutive successes the first time no sequence of consecutive k failures occurs prior, denoted by T^(k). Next, we consider the waiting time for a run of k consecutive failures the first time no sequence of k consecutive successes occurred prior, denoted by J^(k). In addition, we study the distribution of the weighted average. The exact formulae of the probability mass function, mean, and variance of distributions are also obtained.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.43 no.3 s.309
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• pp.34-42
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• 2006

In general, almost information is stored in only a few wavelet coefficients. This sparse characteristic of wavelet coefficient can be modeled by the mixture of Gaussian probability density function and point mass at zero, and denoising for this prior model is peformed by using Bayesian estimation. In this paper, we propose a method of parameter estimation for denoising using hypothesis-testing problem. Hypothesis-testing problem is applied to variance of wavelet coefficient, and $X^2$-test is used. Simulation results show our method outperforms about 0.3dB higher PSNR(peak signal-to-noise ratio) gains compared to the states-of-art denoising methods when using orthogonal wavelets.

• Proceedings of the Korean Statistical Society Conference
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• 2002.05a
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• pp.73-78
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• 2002

In this paper we develop a method for constructing a Bayesian HPD (highest probability density) interval of a ratio of two multivariate normal generalized variances. The method gives a way of comparing two multivariate populations in terms of their dispersion or spread, because the generalized variance is a scalar measure of the overall multivariate scatter. Fully parametric frequentist approaches for the interval is intractable and thus a Bayesian HPD(highest probability densith) interval is pursued using a variant of weighted Monte Carlo (WMC) sampling based approach introduced by Chen and Shao(1999). Necessary theory involved in the method and computation is provided.

• Journal of Korean Society for Quality Management
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• v.30 no.3
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• pp.186-194
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• 2002

In this paper we introduce formulae for estimating the failure rate of a large scaled software by using the Bayesian rule when a black-box random testing which selects an element(test case) at random with equally likely probability, is performed. A program or software can be treated as a mathematical function with a well-defined (input)domain and range. For a large scaled software, their input domains can be partitioned into multiple subdomains and exhaustive testing is not generally practical. Testing is proceeding with selecting a subdomain, and then picking a test case from within the selected subdomain. Whether or not the proportion of selecting one of the subdomains is assumed probability, we developed the formulae either case by using Bayesian rule with gamma distribution as a prior distribution.

• Journal of the Korean Statistical Society
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• v.30 no.1
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• pp.89-98
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• 2001

Brown and Proschan(1983) introduced a model for imperfect repair. At each failure of a device, with probability p, it is repaired completely or replaced with a new device(perfect repair), and with probability 1-p, it is returned to the functioning state, but it is only recovered to its condition just prior to failure(imperfect repair or minimal repair). In this paper, we limit the number of consecutive minimal repairs by n. We find some useful properties about $\mu$$_{k}$, the expected time between the k-th and the (k+1)-st repair under he assumption that only minimal repairs are performed. Then, we assign cost to each repair and find the value of n which minimized the long-run average cost for a fixed p under the condition that the life distribution F os the device is DMRL.L.

• The Korean Journal of Applied Statistics
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• v.7 no.1
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• pp.159-172
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• 1994

An empirical Bayes estimator of the probability of discovering a new species is proposed when some prior information is available on the number f species. The new estimator is shown via simulations to have only a moderate bias and a smaller RMSE than Good's estimator when the species population follows a truncated geometric distribution.

• Journal of Korean Society for Quality Management
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• v.30 no.2
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• pp.118-129
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• 2002

A multiple test of a mean parameter, λ, in the Poisson model is considered using the Bayes factor. Under noninformative improper priors, the intrinsic Bayes factor(IBF) of Berger and Pericchi(1996) and the fractional Bayes factor(FBF) of O'Hagan(1995) called as the default or automatic Bayes factors are used to select one among three models, M$_1$: λ< $λ_0, M$_2$: λ= $λ_0, M$_3$: λ> $λ_0. Posterior probability of each competitive model is computed using the default Bayes factors. Finally, theoretical results are applied to simulated data and real data.

• Communications for Statistical Applications and Methods
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• v.9 no.1
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• pp.129-139
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• 2002

Default Bayesian method for detecting the changes in sequences of independent exponential random variates and independent Poisson random variates is considered. Noninformative priors are assumed for all the parameters in both of change models. Default Bayes factors, AIBF, MIBF, FBF, to check whether there is any change or not on each sequence and the posterior probability densities of change at each time point are derived. Theoretical results discussed in this paper are applied to some numerical data.