• The Korean Journal of Applied Statistics
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• v.24 no.3
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• pp.523-533
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• 2011

Most nancial preference methods for market risk management are to estimate VaR. In many real cases, it happens to obtain the VaRs of the univariate as well as multivariate distributions based on multivariate data. Copula functions are used to explore the dependence of non-normal random variables and generate the corresponding multivariate distribution functions in this work. We estimate Archimedian Copula functions including Clayton Copula, Gumbel Copula, Frank Copula that are tted to the multivariate earning rate distribution, and then obtain their VaRs. With these Copula functions, we estimate the VaRs of both a certain integrated industry and individual industries. The parameters of three kinds of Copula functions are estimated for an illustrated stock data of two Korean industries to obtain the VaR of the bivariate distribution and those of the corresponding univariate distributions. These VaRs are compared with those obtained from other methods to discuss the accuracy of the estimations.

• Journal of the Korean Data and Information Science Society
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• v.25 no.1
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• pp.177-185
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• 2014

Under bivariate normal distribution assumptions, the interaction and quadratic terms are needed in the logistic regression model with two predictors. However, depending on the correlation coefficient and the variances of two conditional distributions, the interaction and quadratic terms may not be necessary. Although the need for these terms can be determined by comparing the two scatter plots, it is not as useful for interaction terms. We explore the structure and usefulness of the 3-D residual plot as a tool for dealing with interaction in logistic regression models. If predictors have an interaction effect, a 3-D residual plot can show the effect. This is illustrated by simulated and real data.

• Journal of Korean Society for Quality Management
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• v.35 no.4
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• pp.147-158
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• 2007

Owing to the rapid growth in automated manufacturing systems, screening inspection becomes an attractive practice for removing nonconforming items, and it has been suggested that inspection will essentially become an inherent part of modem manufacturing processes. In this paper, we propose rectifying screening inspections which allow quality practitioners to use performance and surrogate variables interchangeably in real-time applications. Two screening inspections are considered; a statistically-based screening inspection to reduce the current proportion of nonconforming items to a specified AOQ(average outgoing quality) after screening, and an economically-based screening inspection where the tolerance limit is determined so that the expected total cost is minimized. It is assumed that the performance variable and the surrogate variable are jointly normally distributed. For two screening inspections, methods of finding the optimal solutions are presented and numerical examples are also given.

• Journal of Korea Water Resources Association
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• v.51 no.9
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• pp.747-759
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• 2018

Multivariate regional frequency analysis has advantages of regional and multivariate framework as adopting a large number of regional dataset and modeling phenomena that cannot be considered in the univariate frequency analysis. To the best of our knowledge, the multivariate regional frequency analysis has not been employed for hydrological variables in South Korea. Applicability of the multivariate regional frequency analysis should be investigated for the hydrological variable in South Korea in order to improve our capacity to model the hydrological variables. The current study focused on estimating parameters of regional copula and regional marginal models, selecting the most appropriate distribution models, and estimating regional multivariate growth curve in the multivariate regional frequency analysis. Annual maximum rainfall and duration data observed at 71 stations were used for the analysis. The results of the current study indicate that Frank and Gumbel copula models were selected as the most appropriate regional copula models for the employed regions. Several distributions, e.g. Gumbel and log-normal, were the representative regional marginal models. Based on relative root mean square error of the quantile growth curves, the multivariate regional frequency analysis provided more stable and accurate quantiles than the multivariate at-site frequency analysis, especially for long return periods. Application of regional frequency analysis in bivariate rainfall-duration analysis can provide more stable quantile estimation for hydraulic infrastructure design criteria and accurate modelling of rainfall-duration relationship.

• Communications for Statistical Applications and Methods
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• v.18 no.3
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• pp.377-389
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• 2011

A higher quality level is generally perceived by customers as improved performance by assigning a correspondingly higher satisfaction score. The third generation index $C_{pmk}$ is more powerful than two useful indices $C_p$ and $C_{pk}$ that have been widely used in six sigma industries to assess process performance. In actual manufacturing industries, process capability analysis often entails characterizing or assessing processes or products based on more than one engineering specification or quality characteristic. Since these characteristics are related, it is a risky undertaking to represent the variation of even a univariate characteristic by a single index. Therefore, the desirability of using vector-valued process capability index(PCI) arises quite naturally. In this paper, we consider more powerful vector-valued process capability index $C_{pmk}$ = ($C_{pmkx}$, $C_{pmky}$)$^t$ that consider the univariate process capability index $C_{pmk}$. First, we examine the process capability index $C_{pmk}$ and plug-in estimator $\hat{C}_{pmk}$. In addition, we derive its asymptotic distribution and variance-covariance matrix $V_{pmk}$ for the vector valued process capability index $C_{pmk}$. Under the assumption of bivariate normal distribution, we study asymptotic confidence regions of our vector-valued process capability index $C_{pmk}$ = ($C_{pmkx}$, $C_{pmky}$)$^t$.

• The Korean Journal of Applied Statistics
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• v.29 no.7
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• pp.1201-1212
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• 2016

Value at Risk (VaR) for market risk management is a favorite method used by financial companies; however, there are some problems that cannot be explained for the amount of loss when a specific investment fails. Conditional Tail Expectation (CTE) is an alternative risk measure defined as the conditional expectation exceeded VaR. Multivariate loss rates are transformed into a univariate distribution in real financial markets in order to obtain CTE for some portfolio as well as to estimate CTE. We propose multivariate CTEs using multivariate quantile vectors. A relationship among multivariate CTEs is also derived by extending univariate CTEs. Multivariate CTEs are obtained from bivariate and trivariate normal distributions; in addition, relationships among multivariate CTEs are also explored. We then discuss the extensibility to high dimension as well as illustrate some examples. Multivariate CTEs (using variance-covariance matrix and multivariate quantile vector) are found to have smaller values than CTEs transformed to univariate. Therefore, it can be concluded that the proposed multivariate CTEs provides smaller estimates that represent less risk than others and that a drastic investment using this CTE is also possible when a diversified investment strategy includes many companies in a portfolio.

• Asia-Pacific Journal of Business Venturing and Entrepreneurship
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• v.16 no.6
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• pp.157-175
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• 2021

This study categorized 3,214 companies out of the tech firms supported by the Korea Technology Finance Corporation's "technology guarantee scheme" through technology assessment from 2017 to 2019 into Fourth Industrial Revolution-related companies and general SMEs. The impact of the management characteristics of these 1,752 tech firms on the determination of high-growth firms was then empirically analyzed. This study used the OECD(2007) definition to define a "high-growth firm" as "an enterprise with average revenue growth greater than 20% per annum, over a two-year period." As the two sample groups showed non-normal distribution, this study conducted the Mann-Whitney U test, a nonparametric test, to analyze the mean differences and bivariate logistic regression in which the normality assumption is less stringent. The independent variables include fundamental characteristics; a regional dummy; a technological level dummy; and the capabilities of company representatives, human capital, and technological innovation. The corresponding sub-variables are representatives' level of education and experience in the same industry, full-time workers, research personnel, the extent of intellectual property rights, investment in research and development, firm age, total assets, region_metropolitan area, region_central region, technological level_high technology, and technological level_medium technology. As a result, the research hypothesis about representatives' level of experience in the same industry, full-time workers, total assets, and technological level_high technology was supported for the Fourth Industrial Revolution-related companies. For the general SMEs, the research hypothesis about representatives' level of experience in the same industry, research personnel, total assets, and region_metropolitan area was supported.