• The Korean Journal of Applied Statistics
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• v.12 no.2
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• pp.347-362
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• 1999

강수 형태 및 강수량을 동시에 고려하는 1차의 마코브 연쇄-의존 모델을 고차의 모델로 확장하였다. 남한의 53개 지역의 강수량 자료에 대해 계절별로 마코브 연쇄의 차수를 결정하였고, 고차의 마코브 연쇄-의존 모델을 적용하여 강수량의 분포특성을 살펴 보았다.

• Proceedings of the Korea Water Resources Association Conference
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• 2009.05a
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• pp.1202-1206
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• 2009

본 논문에서는 세계 최장의 기록을 보유하고 있는 서울지점의 강우량 자료를 이용하여 강우 발생특성의 장기 변동성을 분석하였다. 우선 마코브 연쇄에 근거한 전이확률 및 발생특성을 분석하여 측우기 자료의 정확성을 강우의 발생확률적 측면에서 평가하였다. 전이확률 및 발생특성 분석결과 원자료 계열의 CWK와 MRG는 발생특성이 다르게 나타났다. 강우사상의 특성은 과거에 비해 강우사상의 발생빈도가 높아지고 있으며 각 강우사상의 지속기간은 짧아지고 있는 것으로 나타났다. 이러한 결과를 최근 강우량의 증가양상과 더불어 고려하면 강우사상의 빈도와 심도(강우강도)가 증가하는 추세라고 해석할 수 있다.

• The Korean Journal of Applied Statistics
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• v.21 no.4
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• pp.603-613
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• 2008

We often encounter the situation that discrete count data have a large portion of zeros. In this case, it is not appropriate to analyze the data based on standard regression models such as the poisson or negative binomial regression models. In this article, we consider Bayesian analysis for two commonly used models. They are zero-inflated poisson and negative binomial regression models. We use the Bayes factor as a model selection tool and computation is proceeded via Markov chain Monte Carlo methods. Crash count data are analyzed to support theoretical results.

• The Korean Journal of Applied Statistics
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• v.11 no.2
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• pp.377-387
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• 1998

A Markov Chain Monte Carlo method with data augmentation is developed to compute the features of the posterior distribution. For each observed failure epoch, we introduced latent variables that indicates with component of the Superposition model. This data augmentation approach facilitates specification of the transitional measure in the Markov Chain. Metropolis algorithms along with Gibbs steps are proposed to preform the Bayesian inference of such models. for model determination, we explored the Pre-quential conditional predictive Ordinate(PCPO) criterion that selects the best model with the largest posterior likelihood among models using all possible subsets of the component intensity functions. To relax the monotonic intensity function assumptions, we consider in this paper Superposition of Musa-Okumoto and Erlang(2) models. A numerical example with simulated dataset is given.

• The Korean Journal of Applied Statistics
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• v.23 no.1
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• pp.189-196
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• 2010

It is never an easy task to physically randomize the sequence of cards. For instance, US 1970 draft lottery resulted in a social turmoil since the outcome sequence of 366 birthday numbers showed a significant relationship with the input order (Wikipedia, "Draft Lottery 1969", Retrieved 2009/05/01). We are motivated by Laplace's 1825 book titled Philosophical Essay on Probabilities that says "Suppose that the numbers 1, 2, ..., 100 are placed, according to their natural ordering, in an urn, and suppose further that, after having shaken the urn, to shuffle the numbers, one draws one number. It is clear that if the shuffling has been properly done, each number will have the same chance of being drawn. But if we fear that there are small differences between them depending on the order in which the numbers were put into the urn, we can decrease these differences considerably by placing these numbers in a second urn in the order in which they are drawn from the first urn, and then shaking the second urn to shuffle the numbers. These differences, already imperceptible in the second urn, would be diminished more and more by using a third urn, a fourth urn, &c." (translated by Andrew 1. Dale, 1995, Springer. pp. 35-36). Laplace foresaw what would happen to us in 150 years later, and, even more, suggested the possible tool to handle the problem. But he did omit the detailed arguments for the solution. Thus we would like to write the supplement in modern terms for Laplace in this research note. We formulate the problem with a lottery box model, to which Markov chain theory can be applied. By applying Markov chains repeatedly, one expects the uniform distribution on k states as stationary distribution. Additionally, we show that the probability of even-number of successes in binomial distribution with trials and the success probability $\theta$ approaches to 0.5, as n increases to infinity. Our theory is illustrated to the cases of truncated geometric distribution and the US 1970 draft lottery.