• The Korean Journal of Applied Statistics
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• v.29 no.2
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• pp.301-308
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• 2016

The process capability index is used to determine whether a production process is capable of producing items within a specified tolerance. Some process capability indices $C_p$, $C_{pk}$ and $C_{pm}$ have been of particular interest as useful management tools for tracking process performance. Most evaluations on process capability indices focus on statistical estimation and test of hypothesis. It is necessary to investigate their asymptotic correlationship among basic estimators ${\hat{C}}_p$, ${\hat{C}}_{pk}$ and ${\hat{C}}_{pm}$ of process capability indices $C_p$, $C_{pk}$ and $C_{pm}$. In this paper, we study their asymptotic correlationship for three process capability indices ${\hat{C}}_p$, ${\hat{C}}_{pk}$ and ${\hat{C}}_{pm}$ under bivariate normal distribution BN(${\mu}_x,{\mu}_y,{\sigma}^2_x,{\sigma}^2_y,{\rho}$). With some nonnormal processes, the asymptotic correlation coefficient of any two respective process capability index estimators could be established.

• Proceedings of the Korea Water Resources Association Conference
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• 2010.05a
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• pp.600-604
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• 2010

수문설계 인자인 확률홍수량 산정시 짧은 홍수량 자료 길이로 인해 홍수량을 직접 이용하기 보다는 강우자료와 강우-유출모형에 의존하고 있는 현시점에서 무엇보다 중요한 것은 신뢰할 만한 확률강우량이 산정되어야 한다는 것이다. 하지만 지금까지의 강우빈도해석(rainfall frequency analysis)은 강도(intensity), 지속기간(duration), 깊이(depth) 사이의 연관성은 고려하지 않은 단편적인 방법론에 그치고 있다. 즉, 강우를 표현하는 인자들 간 독립(independency)이라는 가정을 거친 후, 간단한 단변량(univariate) 강우빈도분포(rainfall frequency distribution)로 확률강우량을 산정하고 있다는 것이다. 간단한 모형에 따른 이점은 있으나 최근의 강우 형태는 매우 복잡한 양상을 띠고 있어, 단변량 강우빈도분포로 이를 대표하기에는 무리가 따른다. 따라서 본 연구에서는 강우빈도해석의 인자가 독립적이며 정규분포(normal distribution)라 가정하지 않고, 세 개의 주변 분포(marginal distribution)의 형태가 같지 않다는 점, 또한 가정하지 않는 방법론 중, 그 가치를 널리 인정받고 있는 Archimedean Copula (AC)에 대한 연구를 수행하였다. AC를 이용하여 강도, 지속기간, 깊이 사이의 종속성 중, 두 가지 변량을 고려한 이변량(bivariate) 강우빈도해석을 수행하였고 그 효용성을 검토해 보았다.

• Tunnel and Underground Space
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• v.12 no.1
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• pp.19-30
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• 2002

Rock joint orientation is one of important geometric attributes that have an influence on the stability of rock structures such as rock slopes and tunnels. Especially, statistical models of the geometric attributes of rock joints can provide a probabilistic approach of rock engineering problems. The result from probabilistic modeling relies on the choice of statistical model. Therefore, it is critical to define a representative statistical model for joint orientation data as well as joint size and intensity and build up a series of modeling procedure including analytical validation. In this paper, we have examined a theoretical methodology for the statistical estimate and hypothesis analysis based upon Fisher distribution and bivariate normal distribution. In addition, we have proposed the algorithms of random number generator which is applied to the simulation of rock joint networks and risk analysis.

• Journal of the Korean Data and Information Science Society
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• v.23 no.4
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• pp.797-805
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• 2012

Many circular distributions are known to be not only asymmetric but also bimodal. Hidden truncation method of generating asymmetric distribution is applied to a bivariate circular distribution to generate an asymmetric circular distribution. While many other existing asymmetric circular distributions can only model an asymmetric data, this new circular model has great flexibility in terms of asymmetry and bi-modality. Some properties of the new model, such as the trigonometric moment generating function, and asymptotic inference about the truncation parameter are presented. Simulation and real data examples are provided at the end to demonstrate the utility of the novel distribution.

• Water for future
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• v.27 no.1
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• pp.133-140
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• 1994

The augmenting hydrologic data using a correlation procedue has been used to improve the estimates of the mean and variance at the site of interest with short record when one or more nearby sites with longer records are available. The variance of the unbiased maximum likelihood estimator of ${{\sigma}_v}^2$ derived by Moran based on the multivariate normal distribution is modified into the form of Matalas and jacobs for the bivariate normal distribution to get the critical minimum values of the multiple correlation coefficient which give the improvement for estimation the variance at the site of interest. Those values are tabulated for various lengths of records and the number of sites.

• Proceedings of the Korea Concrete Institute Conference
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• 2001.05a
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• pp.795-800
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• 2001

Two evaluation techniques of the tunnel lining concrete using ultra sonic velocity method are developed. Modified linear regression technique is proposed to enhance the corelation between the pulse velocity and the compressive strength of core specimens. And bivariate normal distribution is assumed to evaluate the quality of concrete as a terms of compressive strength. A simple corelation table between the pulse velocity and the compressive strength of core specimens are proposed.

• Journal of Korean Institute of Industrial Engineers
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• v.27 no.2
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• pp.135-139
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• 2001

A process control procedure is suggested when screening inspection is performed with a surrogate variable correlated with the performance variable. Assuming bivariate normal distribution for the performance and screening variable, the procedure is designed on the basis of the time required for detecting process shift.

• KDI Journal of Economic Policy
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• v.32 no.3
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• pp.71-99
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• 2010

The concept of CoVaR introduced by Adrian and Brunnermeier (2009) is a useful tool to measure the risk spillover effect. It can capture the risk contribution of each institution to overall systemic risk. While Adrian and Brunnermeier rely on the quantile regression method in the estimation of CoVaR, we propose a new estimation method using parametric distribution functions such as bivariate normal and $S_U$-normal distribution functions. Based on our estimates of CoVaR for Korean banking industry, we investigate the practical usefulness of CoVaR for a systemic risk measure, and compare the estimation performance of each model. Empirical results show that bank makes a positive contribution to system risk. We also find that quantile regression and normal distribution models tend to considerably underestimate the CoVaR (in absolute value) compared to $S_U$-normal distribution model, and this underestimation becomes serious when the crisis in a financial system is assumed.

• Journal of Korean Society of Forest Science
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• v.88 no.3
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• pp.400-407
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• 1999

The purpose of thin paper is to test difference of the two question formats, open-ended and dichotomous choice formats, in the contingent valuation method using the estimated recreational benefits. The data were collected from the visitors at the Songnisan National Park. The recreational benefit based on the equivalent variation. The two question formats, but the same content, were asked of the same individuals. In this analysis, it was used travel cost and monthly income as the exogenous variables, which assumed a linear functional form for the WTP equation. The model assumed a bivariate normal distribution on the basis of the probit and tobit model concerning the censored zero WTP. The result showed no differences in the recreational benefits from the different question formats under a same respondent. The mean benefit was estimated 25.556 Won per 5 years per visitors.

• Communications for Statistical Applications and Methods
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• v.28 no.1
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• pp.59-79
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• 2021

Value at Risk (VaR) is one of the most common risk management tools in finance. Since a portfolio of several assets, rather than one asset portfolio, is advantageous in the risk diversification for investment, VaR for a portfolio of two or more assets is often used. In such cases, multivariate distributions of asset returns are considered to calculate VaR of the corresponding portfolio. Copulas are one way of generating a multivariate distribution by identifying the dependence structure of asset returns while allowing many different marginal distributions. However, they are used mainly for bivariate distributions and are not widely used in modeling joint distributions for many variables in finance. In this study, we would like to examine the performance of various copulas for high dimensional data and several different dependence structures. This paper compares copulas such as elliptical, vine, and hierarchical copulas in computing the VaR of portfolios to find appropriate copula functions in various dependence structures among asset return distributions. In the simulation studies under various dependence structures and real data analysis, the hierarchical Clayton copula shows the best performance in the VaR calculation using four assets. For marginal distributions of single asset returns, normal inverse Gaussian distribution was used to model asset return distributions, which are generally high-peaked and heavy-tailed.