• Journal of the Korean Data and Information Science Society
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• v.19 no.4
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• pp.1379-1390
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• 2008

This article deals with the problem of testing the difference of quantiles in exponential distributions. We propose Bayesian hypothesis testing procedures for the difference of two quantiles under the noninformative prior. The noninformative prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. So we propose the objective Bayesian hypothesis testing procedures based on the fractional Bayes factor and the intrinsic Bayes factor under the matching prior. Simulation study and a real data example are provided.

• Communications for Statistical Applications and Methods
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• v.11 no.3
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• pp.447-454
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• 2004

In this paper, we consider the bootstrap method to the interval estimation of the difference of quantiles of right censored data. We showed the validity of bootstrap method and compare with others with real data example. In simulation various resampling schemes for right censored data are also considered.

• Communications for Statistical Applications and Methods
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• v.14 no.2
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• pp.431-442
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• 2007

In this paper, we develop the noninformative priors when the parameter of interest is the difference between quantiles of two exponential distributions. We want to develop the first and second order probability matching priors. But we prove that the second order probability matching prior does not exist. It turns out that Jeffreys' prior does not satisfy the first order matching criterion. The Bayesian credible intervals based on the first order probability matching prior meet the frequentist target coverage probabilities much better than the frequentist intervals of Jeffreys' prior. Some simulation and real example will be given.

• Journal of the Korean Society of Hazard Mitigation
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• v.7 no.5
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• pp.79-88
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• 2007

This study evaluated the statistical stationarity of rainfall quantiles as well as the rainfall itself. The conventional methodologies like the Cox-Stuart test for trend and Dickey-Fuller test for a unit root used for testing the stationarity of a time series were applied and evaluated their application to the rainfall quantiles. As results, first, no obvious increasing or decreasing trend was found for the rainfall in Seoul, which was also found to be a stationary time series based on the Dickey-Fuller test. However, the Cox-Stuart test for the rainfall quantiles show some trends but not in consistent ways of increasing or decreasing. Also, the Dickey-Fuller test for a unit root shows that the rainfall quantiles are non-stationary. This result is mainly due to the difference between the rainfall data and rainfall quantiles. That is, the rainfall is a random variable without any trend or non-stationarity. On the other hand, the rainfall quantiles are estimated by considering all the data to result in high correlation between their consecutive estimates. That is, as the rainfall quantiles are estimated by adding a stationary rainfall data continuously, it becomes possible for their consecutive estimates to become highly correlated. Thus, it is natural for the rainfall quantiles to be decided non-stationary if considering the methodology used in this study.

• Journal of the Korean Statistical Society
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• v.22 no.2
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• pp.159-169
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• 1993

In this article, we consider two sample problem with randomly right censored data. We propse two-sample confidence intervals for the difference in medians or any quantiles, based on bootstrap. The bootstrap version of two-sample confidence intervals proposed in this article is simple to apply and do not need the assumption of the shift model, so that for the non-shift model, the density estimation is not necessary, which is an attractive feature in small to moderate sized sample case.

• Journal of the Korean Data and Information Science Society
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• v.28 no.6
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• pp.1457-1469
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• 2017

Private education expenses is one of the key issues in Korea and there have been many discussions about it. Academically, most of previous researches for private education expenses have used multiple regression linear model based on ordinary least squares (OLS) method. However, if the data do not satisfy the basic assumptions of the OLS method such as the normality and homoscedasticity, there is a problem with the reliability of estimations of parameters. In this case, quantile regression model is preferred to OLS model since it does not depend on the assumptions of nonnormality and heteroscedasticity for the data. In the present study, the data from a survey on private education expenses, conducted by Statistics Korea in 2015 has been analyzed for investigation of the impacting factors for private education expenses. Since the data do not satisfy the OLS assumptions, quantile regression model has been employed in Bayesian approach by using gibbs sampling method. The analysis results show that the gender of the student, parent's age, and the time and cost of participating after school are not significant. Household income is positively significant in proportion to the same size for all levels (quantiles) of private education expenses. Spending on private education in Seoul is higher than other regions and the regional difference grows as private education expenditure increases. Total time for private education and student's achievement have positive effect on the lower quantiles than the higher quantiles. Education level of father is positively significant for midium-high quantiles only, but education level of mother is for all but low quantiles. Participating after school is positively significant for the lower quantiles but EBS textbook cost is positively significant for the higher quantiles.

• Communications for Statistical Applications and Methods
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• v.12 no.2
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• pp.395-411
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• 2005

In this paper, we develop the Jeffreys' prior, reference prior and the the probability matching priors for the difference of intraclass correlation coefficients in familial data. e prove the sufficient condition for propriety of posterior distributions. Using marginal posterior distributions under those noninformative priors, we compare posterior quantiles and frequentist coverage probability.

• Communications for Statistical Applications and Methods
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• v.6 no.1
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• pp.237-249
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• 1999

It has been issued that the irreconcilability of the classical test for a point null and standard Bayesian formulation for testing such a point null. The infimum of the posterior probability of the null hypothesis is used as measure of evidence against the null hypothesis in Bayesian approach; here the infimum is over the family of priors on the alternative hypotheses which includes all density that are a priori reasonable. For iid observations from a multivariate normal distribution in $\textit{p}$ dimensions with an unknown mean and a covariance matrix propotional to the Identity we consider the difference and the Wolfowitz distance of the distributions of the P-value and the lower bound of the posterior probability over the family of all normal priors. The Wolfowitz distance is interpreted as the average difference of the quantiles of the two distrbutions.

• Journal of the Korean Society of Hazard Mitigation
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• v.11 no.2
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• pp.137-146
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• 2011

In this study, annual maximum storm events are evaluated by applying the bivariate extremal distribution. Rainfall quantiles of probabilistic storm event are calculated using OR case joint return period, AND case joint return period and interval conditional joint return period. The difference between each of three joint return periods was explained by the quadrant which shows probability calculation concept in the bivariate frequency analysis. Rainfall quantiles under AND case joint return periods are similar to rainfall depths in the univariate frequency analysis. The probabilistic storm events overcome the primary limitation of conventional univariate frequency analysis. The application of these storm event analysis provides a simple, statistically efficient means of characterizing frequency of extreme storm event.

• Journal of the Korean earth science society
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• v.44 no.4
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• pp.255-263
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• 2023

Western coastal area of Chungnam, including Cheonsu Bay and Garorim Bay, has suffered from hot and cold extremes. In this study, the extreme sea surface temperature on the western coast of Chungnam was analyzed using the quantile regression method, which extracts the linear regression values in all quantiles. The regional MOHID (MOdelo HIDrodinâmico) model, with a high resolution on a 1/60° grid, was constructed to reproduce the extreme sea surface temperature. For future prediction, the SSP5-8.5 scenario data of the CMIP6 model were used to simulate sea surface temperature variability. Results showed that the extreme sea surface temperature of Cheonsu Bay in August 2017 was successfully simulated, and this extreme sea surface temperature had a significant negative correlation with the Pacific decadal variability index. As a result of future climate prediction, it was found that an average of 2.9℃ increased during the simulation period of 86 years in the Chungnam west coast and there was a seasonal difference (3.2℃ in summer, 2.4℃ in winter). These seasonal differences indicate an increase in the annual temperature range, suggesting that extreme events may occur more frequently in the future.