• Title/Summary/Keyword: bivariate normal distribution model

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A Comparison of the Different Question Formats in the Contingent Valuation Method for the Evaluation of Recreational Benefit (휴양자원가치(休養資源價値) 평가(評價)를 위한 CVM 질문형(質問型) 비교(比較))

  • Kim, Joon-Soon
    • 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.

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Estimating the CoVaR for Korean Banking Industry (한국 은행산업의 CoVaR 추정)

  • Choi, Pilsun;Min, Insik
    • 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.

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Study on Estimating the Optimal Number-right Score in Two Equivalent Mathematics-test by Linear Score Equating (수학교과의 동형고사 문항에서 양호도 향상에 유효한 최적정답율 산정에 관한 연구)

  • 홍석강
    • The Mathematical Education
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    • v.37 no.1
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    • pp.1-13
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    • 1998
  • In this paper, we have represented the efficient way how to enumerate the optimal number-right scores to adjust the item difficulty and to improve item discrimination. To estimate the optimal number-right scores in two equivalent math-tests by linear score equating a measurement error model was applied to the true scores observed from a pair of equivalent math-tests assumed to measure same trait. The model specification for true scores which is represented by the bivariate model is a simple regression model to inference the optimal number-right scores and we assume again that the two simple regression lines of raw scores and true scores are independent each other in their error models. We enumerated the difference between mean value of $\chi$* and ${\mu}$$\_$$\chi$/ and the difference between the mean value of y*and a+b${\mu}$$\_$$\chi$/ by making an inference the estimates from 2 error variable regression model. Furthermore, so as to distinguish from the original score points, the estimated number-right scores y’$\^$*/ as the estimated regression values of true scores with the same coordinate were moved to center points that were composed of such difference values with result of such parallel score moving procedure as above mentioned. We got the asymptotically normal distribution in Figure 5 that was represented as the optimal distribution of the optimal number-right scores so that we could decide the optimal proportion of number-right score in each item. Also by assumption that equivalence of two tests is closely connected to unidimensionality of a student’s ability. we introduce new definition of trait score to evaluate such ability in each item. In this study there are much limitations in getting the real true scores and in analyzing data of the bivariate error model. However, even with these limitations we believe that this study indicates that the estimation of optimal number right scores by using this enumeration procedure could be easily achieved.

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Value at Risk of portfolios using copulas

  • Byun, Kiwoong;Song, Seongjoo
    • 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.

A Study on a Hit Probability Model for Polygonal Target (다각형 표적의 명중확률 산정모델의 연구)

  • 황흥석
    • Journal of the military operations research society of Korea
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    • v.25 no.1
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    • pp.160-168
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    • 1999
  • This research focussed on developing a hit probability model for polygonal target to increase the survivability of weapon systems by its shape design. First, we defined the delivery errors and derived functions for these errors based on the assumption of bivariate normal distribution, and the derived functions for probability of shot hitting of various shapes of polygonal target. Also, we developed computer program for computation of the probability of hitting a general n-sided polygon and we have shown a sample run output. The model could be used to improve the survivability from design phase by designing optimal polygonal shape of weapon system.

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Multiple Change-Point Estimation of Air Pollution Mean Vectors

  • Kim, Jae-Hee;Cheon, Sooy-Oung
    • The Korean Journal of Applied Statistics
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    • v.22 no.4
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    • pp.687-695
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    • 2009
  • The Bayesian multiple change-point estimation has been applied to the daily means of ozone and PM10 data in Seoul for the period 1999. We focus on the detection of multiple change-points in the ozone and PM10 bivariate vectors by evaluating the posterior probabilities and Bayesian information criterion(BIC) using the stochastic approximation Monte Carlo(SAMC) algorithm. The result gives 5 change-points of mean vectors of ozone and PM10, which are related with the seasonal characteristics.

Exploring interaction using 3-D residual plots in logistic regression model (3차원 잔차산점도를 이용한 로지스틱회귀모형에서 교호작용의 탐색)

  • Kahng, Myung-Wook
    • 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.

Bivariate regional frequency analysis of extreme rainfalls in Korea (이변량 지역빈도해석을 이용한 우리나라 극한 강우 분석)

  • Shin, Ju-Young;Jeong, Changsam;Ahn, Hyunjun;Heo, Jun-Haeng
    • 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.