• Communications for Statistical Applications and Methods
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• v.26 no.1
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• pp.35-46
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• 2019

Multivariate Confidence Region (MCR) cannot be used to obtain the confidence region of the mean vector of multivariate data when the normality assumption is not satisfied; however, the Quantile Confidence Region (QCR) could be used with a Multivariate Quantile Vector in these cases. The coverage rate of the QCR is better than MCR; however, it has a disadvantage because the QCR has a wide shape when the probability density function follows a bimodal form. In this study, we propose a Quantile Confidence Region using the Highest density (QCRHD) method with the Highest Density Region (HDR). The coverage rate of QCRHD was superior to MCR, but is found to be similar to QCR. The QCRHD is constructed as one region similar to QCR when the distance of the mean vector is close. When the distance of the mean vector is far, the QCR has one wide region, but the QCRHD has two smaller regions. Based on these features, it is found that the QCRHD can overcome the disadvantages of the QCR, which may have a wide shape.

• Journal of Radiation Protection and Research
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• v.29 no.4
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• pp.221-230
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• 2004

The probability of causation(PC) is the measure to ascertain the likelihood that a particular cancer may be attributed to a particular prior exposure to radiation. Since the PC is involved in several uncertainties, it is desirable to use the confidence limit for the PC, not a point estimate for determining whether to award compensation. We developed the program for estimating the PC to Korean radiation workers with cancer, the so-called RHRI-PEPC, which is based on the most reasonable model for radiation cancer risk and recent Korean baseline data. RHRI-PEPC gives us the upper confidence limit for the PC after adjusting several uncertainties and therefore we can assess more reasonably the causality of radiation exposure for cancer occurred in Korean radiation workers.

• Journal of the Korean Society of Hazard Mitigation
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• v.9 no.6
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• pp.143-151
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• 2009

Extreme hydrologic events cause serious disaster, such as flood and drought. Many researchers have an effort to estimate design rainfalls or discharges. This study evaluated parameter estimation methods to estimate probability rainfalls with low uncertainty which will be used in design rainfalls. This study collected rainfall data from Incheon, Gangnueng, Gwangju, Busan, and Chupungryong gage station, and generated synthetic rainfall data using ARMA model. This study employed the maximum likelihood method and the Bayesian inference method for estimating parameters of the Gumbel and GEV distribution. Using a bootstrap resampling method, this study estimated the confidence intervals of estimated probability rainfalls. Based on the comparison of the confidence intervals, this study recommended a proper parameter estimation method for estimating probability rainfalls which have a low uncertainty.

• Journal of Korean Society for Quality Management
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• v.42 no.2
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• pp.199-208
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• 2014

Purpose: This paper explains how to obtain the Bayes estimates of the whole launch vehicle and of a vehicle stage, respectively, for a newly developed expendable launch vehicle. Methods: We determine the parameters of the beta prior distribution using the upper bound of the 60% Clopper-Pearson confidence interval of failure probability which is calculated from previous launch data considering the experience of the developer. Results: Probability that a launch vehicle developed from an inexperienced developer succeeds in the first launch is obtained by about one third, which is much smaller than that estimated from the previous research. Conclusion: The proposed approach provides a more conservative estimate than the previous noninformative prior, which is more reasonable especially for the initial reliability of a new vehicle which is developed by an inexperienced developer.

• Communications for Statistical Applications and Methods
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• v.5 no.3
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• pp.905-926
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• 1998

We propose a modified mid P-value method to reduce the conservativeness for the inference of conditional associations in three-way contingency tables. This improves the ordinary mfd P-value method. For $2{\times} 2${\times} K$ tables, we propose confidence intervals for an assumed common odds ratio based on inverting two separate one-sided tests using the modified mid P-value. Also, an alternative and usually even better ways of constructing intervals, based on Inverting a two-sided test, are presented. The actual probability of coverage of a 100($1-\alpha$)% confidence interval is centered about the nominal level, but the modified mid P-value approach gives actual coverage probability even closer to the nominal level than the ordinary mid P-value approach.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.4
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• pp.141-150
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• 1993

For the three parameter Weibull distribution, the parameter estimation techniques are applied and the asymptotic variances of the quantile to obtain the confidence limits for a given return period are derived. Three estimation techniques are used for these purposes: the methods of moments, maximum likelihood and probability weighted moments. The three parameter Weibull distribution as a flood frequency model is applied to actual flood data.

• Journal of the Korean Statistical Society
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• v.32 no.3
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• pp.299-309
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• 2003

Let ${\pi}_1,...,{\pi}_{k}$k($\geq$2) independent logistic populations such that the cumulative distribution function (cdf) of an observation from the population ${\pi}_{i}$ is $$F_{i}\;=\; {\frac{1}{1+exp{-\pi(x-{\mu}_{i})/(\sigma\sqrt{3})}}},\;$\mid$x$\mid$<\;{\infty}$$ where ${\mu}_{i}(-{\infty}\; < \; {\mu}_{i}\; <\; {\infty}$ is unknown location mean and ${\delta}^2$ is known variance, i ＝ 1,..., $textsc{k}$. Let ${\mu}_{[k]}$ be the largest of all ${\mu}$'s and the population ${\pi}_{i}$ is defined to be 'good' if ${\mu}_{i}\;{\geq}\;{\mu}_{[k]}\;-\;{\delta}_1$, where ${\delta}_1\;>\;0$, i = 1,...,$textsc{k}$. A selection procedure based on sample median is proposed to select a subset of $textsc{k}$ logistic populations which includes all the good populations with probability at least $P^{*}$(a preassigned value). Simultaneous confidence intervals for the differences of location parameters, which can be derived with the help of proposed procedures, are discussed. If a population with location parameter ${\mu}_{i}\;<\;{\mu}_{[k]}\;-\;{\delta}_2({\delta}_2\;>{\delta}_1)$, i ＝ 1,...,$textsc{k}$ is considered 'bad', a selection procedure is proposed so that the probability of either selecting a bad population or omitting a good population is at most 1­ $P^{*}$.

• Communications for Statistical Applications and Methods
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• v.18 no.4
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• pp.445-455
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• 2011

Although misclassified binary data occur frequently in practice, the statistical methodology available for the data is rather limited. In particular, the interval estimation of population proportion has relied on the classical Wald method. Recently, Lee and Choi (2009) developed a new confidence interval by applying the Agresti-Coull's approach and showed the efficiency of their proposed confidence interval numerically, but a theoretical justification has not been explored yet. Therefore, a Bayesian model for the misclassified binary data is developed to consider the Agresti-Coull confidence interval from a theoretical point of view. It is shown that the Agresti-Coull confidence interval is essentially a Bayesian confidence interval.

• Proceedings of the Korean Statistical Society Conference
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• 2003.10a
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• pp.245-252
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• 2003

• Journal of Educational Research in Mathematics
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• v.17 no.2
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• pp.179-199
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• 2007

The purpose of this study was to discover differences between mathematically gifted students (MGS) and non-gifted students (NGS) when making probability judgments. For this purpose, the following research questions were selected: 1. How do MGS differ from NGS when making probability judgments(answer correctness, answer confidence)? 2. When tackling probability problems, what effect do differences in probability judgment factors have? To solve these research questions, this study employed a survey and interview type investigation. A probability test program was developed to investigate the first research question, and the second research question was addressed by interviews regarding the Program. Analysis of collected data revealed the following results. First, both MGS and NGS justified their answers using six probability judgment factors: mathematical knowledge, use of logical reasoning, experience, phenomenon of chance, intuition, and problem understanding ability. Second, MGS produced more correct answers than NGS, and MGS also had higher confidence that answers were right. Third, in case of MGS, mathematical knowledge and logical reasoning usage were the main factors of probability judgment, but the main factors for NGS were use of logical reasoning, phenomenon of chance and intuition. From findings the following conclusions were obtained. First, MGS employ different factors from NGS when making probability judgments. This suggests that MGS may be more intellectual than NGS, because MGS could easily adopt probability subject matter, something not learnt until later in school, into their mathematical schemata. Second, probability learning could be taught earlier than the current elementary curriculum requires. Lastly, NGS need reassurance from educators that they can understand and accumulate mathematical reasoning.