• Journal of the Korean Data and Information Science Society
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• 제27권4호
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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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• 제23권3호
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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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• 제42권3호
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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.

• 대한전자공학회논문지SP
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• 제43권3호
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• pp.34-42
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• 2006

일반적으로 웨이블릿 계수는 적은 수의 계수에 거의 대부분의 정보가 저장되어 있다. 이러한 웨이블릿 계수의 성긴 특성은 가우스 확률밀도 함수와 영점에서의 점 질량(point mass) 함수의 혼합으로 모델링될 수 있으며, 이 프라이어(prior) 모델에 대한 베이지안 추정법으로 잡음 제거를 수행한다. 본 논문에서는 가설-검증 기법을 이용하여 잡음 제거를 위한 파라미터를 추정하는 방법을 제안한다. 가설-검증은 관찰된 웨이블릿 계수의 분산에 적용되며, $X^2$-검증을 사용한다. 모의실험 결과를 통하여 본 논문의 방법이 직교 웨이블릿 변환을 사용한 최신의 잡음 제거 방법보다 대략 0.3dB 정도 우수한 PSNR(peak signal-to-noise ratio) 성능을 나타낸다.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2002년도 춘계 학술발표회 논문집
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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.

• 품질경영학회지
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• 제30권3호
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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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• 제30권1호
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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.

• 응용통계연구
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• 제7권1호
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• pp.159-172
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• 1994

여러개의 종으로 구성된 모집단으로부터 일정 크기의 표본을 추출한 경우 다음에 관측된 종이 신종일 확률에 대한 추정량으로 가장 널리 사용되어 온 것은 Good의 추정량이다. 본 논문에서는 종의 총 수효에 관한 사전정보가 존재할 경우 Good의 추정량에 대한 대안으로서 새로운 경험적 베이지안 추정량을 제안하였다. 모집단이 절단 기하분포를 따를 경우의 소표본 시뮬레이션 결과는 새로운 추정량의 편의가 별로 크지 않으며 RMSE가 Good의 추정량보다 작음을 보여 주었다.

• 품질경영학회지
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• 제30권2호
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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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• 제9권1호
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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.