• Title/Summary/Keyword: generalized normal distribution

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Optimal Thresholds from Mixture Distributions (혼합분포에서 최적분류점)

  • Hong, Chong-Sun;Joo, Jae-Seon;Choi, Jin-Soo
    • The Korean Journal of Applied Statistics
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    • v.23 no.1
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    • pp.13-28
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    • 2010
  • Assuming a mixture distribution for credit evaluation studies, we discuss estimating threshold methods to minimize errors that default borrowers are predicted as non defaults or non defaults are regarded as defaults. A method by using statistical hypotheses tests, the most powerful test and generalized likelihood ratio test, for the probability density functions which are defined with the score random variable and the parameter space consisted of only two elements such as the default and non default states is proposed to estimate a threshold. And anther optimal thresholds to maximize classification accuracy measures of the accuracy and the true rate for ROC and CAP curves are estimated as equations related with these probability density functions. Three kinds of optimal thresholds in terms of the hypotheses testing, the accuracy and the true rate are obtained from normal random samples with various means and variances. The sums of the type I and type II errors corresponding to each optimal threshold are obtained and compared. Finally we discuss about their efficiency and derive conclusions.

Performance of VaR Estimation Using Point Process Approach (점과정 기법을 이용한 VaR추정의 성과)

  • Yeo, Sung-Chil;Moon, Seoung-Joo
    • The Korean Journal of Applied Statistics
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    • v.23 no.3
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    • pp.471-485
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    • 2010
  • VaR is used extensively as a tool for risk management by financial institutions. For convenience, the normal distribution is usually assumed for the measurement of VaR, but recently the method using extreme value theory is attracted for more accurate VaR estimation. So far, GEV and GPD models are used for probability models of EVT for the VaR estimation. In this paper, the PP model is suggested for improved VaR estimation as compared to the traditonal EV models such as GEV and GPD models. In view of the stochastic process, the PP model is regarded as a generalized model which include GEV and GPD models. In the empirical analysis, the PP model is shown to be superior to GEV and GPD models for the performance of VaR estimation.

Effect of Socioeconomic Status on Healthcare Utilization in Patients with Rare and Incurable Diseases (희귀난치성질환자에서 사회경제적 수준이 의료이용에 미치는 영향)

  • Im, Jun;Kim, Myeong-Hee;Im, Jeong-Soo;Oh, Dae-Gyu
    • Health Policy and Management
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    • v.19 no.4
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    • pp.66-77
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    • 2009
  • This study aims to examine the effect of socioeconomic status (hereafter, SES) on healthcare utilization of the patients with rare and incurable diseases. Information of 2,973 patients who were self-employed insured and utilized healthcare service in 2007 was drawn from the National Health Insurance (hereafter, NHI) claim data. SES was set as four groups based on the monthly contribution. Outcome variable was the expense for outpatient and in-hospital services, which was log-transformed and square-rooted in oder to obtain normal distribution. Covariates included age, gender, residence and diagnosis. To examine the effects after controlling for covariates, we employed generalized estimating equation model, since patients with the same diagnosis are likely to have similar characteristics of demographics and healthcare utilization. Univariate statistics showed that lower SES was associated with less utilization of healthcare services. After controlling for covariates, a significantly smaller amount of money was expended for the lowest SES group compared to the highest one. Rural residence was associated with less utilization, except that residents in Seoul significantly more utilized outpatient services in tertiary hospitals. Considering that there is a subsidy program for the low income patients, such differences in healthcare utilization according to SES seems to result from the burden of out-of-pocket payments for uncovered services of the NHI.

Analysis of the Variation Pattern of the Wave Climate in the Sokcho Coastal Zone (속초 연안의 파랑환경 변화양상 분석)

  • Cho, Hong-Yeon;Jeong, Weon-Mu;Baek, Won-Dae;Kim, Sang-Ik
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.24 no.2
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    • pp.120-127
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    • 2012
  • Exploratory data analysis was carried out by using the long-term wave climate data in Sokcho coastal zone. The main features found in this study are as follows. The coefficient of variations on the wave height and period are about 0.11 and 0.02, respectively. It also shows that the annual components of the wave height and period are dominant and their amplitudes are 0.24 m and 0.56 seconds, respectively. The amount of intra-annual variation range is about two times greater than that of the inter-annual variation range. The distribution shapes of the wave data are very similar to the log-normal and GEV(generalized extreme value) functions. However, the goodness-of-fit tests based on the KS test show as "rejected" for all suggested density functions. Then, the structure of the timeseries wave height data is roughly estimated as AR(3) model. Based on the wave duration results, it is clearly shown that the continuous and maximum duration is decreased as a power function shape and the total duration is exponentially decreased. Meanwhile, the environment of the Sokcho coastal zone is classified as a wave-dominated environment.

Effect and uncertainty analysis according to input components and their applicable probability distributions of the Modified Surface Water Supply Index (Modified Surface Water Supply Index의 입력인자와 적용 확률분포에 따른 영향과 불확실성 분석)

  • Jang, Suk Hwan;Lee, Jae-Kyoung;Oh, Ji Hwan;Jo, Joon Won
    • Journal of Korea Water Resources Association
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    • v.50 no.7
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    • pp.475-488
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    • 2017
  • To simulate accurate drought, a drought index is needed to reflect the hydrometeorological phenomenon. Several studies have been conducted in Korea using the Modified Surface Water Supply Index (MSWSI) to simulate hydrological drought. This study analyzed the limitations of MSWSI and quantified the uncertainties of MSWSI. The influence of hydrometeorological components selected as the MSWSI components was analyzed. Although the previous MSWSI dealt with only one observation for each input component such as streamflow, ground water level, precipitation, and dam inflow, this study included dam storage level and dam release as suitable characteristics of the sub-basins, and used the areal-average precipitation obtained from several observations. From the MSWSI simulations of 2001 and 2006 drought events, MSWSI of this study successfully simulated drought because MSWSI of this study followed the trend of observing the hydrometeorological data and then the accuracy of the drought simulation results was affected by the selection of the input component on the MSWSI. The influence of the selection of the probability distributions to input components on the MSWSI was analyzed, including various criteria: the Gumbel and Generalized Extreme Value (GEV) distributions for precipitation data; normal and Gumbel distributions for streamflow data; 2-parameter log-normal and Gumbel distributions for dam inflow, storage level, and release discharge data; and 3-parameter log-normal distribution for groundwater. Then, the maximum 36 MSWSIs were calculated for each sub-basin, and the ranges of MSWSI differed significantly according to the selection of probability distributions. Therefore, it was confirmed that the MSWSI results may differ depending on the probability distribution. The uncertainty occurred due to the selection of MSWSI input components and the probability distributions were quantified using the maximum entropy. The uncertainty thus increased as the number of input components increased and the uncertainty of MSWSI also increased with the application of probability distributions of input components during the flood season.

The Effect of Weather and Season on Pedestrian Volume in Urban Space (도시공간에서 날씨와 계절이 보행량에 미치는 영향)

  • Lee, Su-mi;Hong, Sungjo
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.20 no.9
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    • pp.56-65
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    • 2019
  • This study empirically analyzes the effect of weather on pedestrian volume in an urban space. We used data from the 2009 Seoul Flow Population Survey and constructed a model with the pedestrian volume as a dependent variable and the weather and physical environment as independent variables. We constructed 28 models and compared the results to determine the effects of weather on pedestrian volume by season, land use, and time zone. A negative binomial regression model was used because the dependent variable did not have a normal distribution. The results show that weather affects the volume of walking. Rain reduced walking volume in most models, and snow and thunderstorms reduced the volume in a small number of models. The effects of the weather depended on the season and land use, and the effects of environmental factors depended on the season. The results have various policy implications. First, it is necessary to provide semi-outdoor urban spaces that can cope with snow or rain. Second, it is necessary to have different policies to encourage walking for each season.

National Survey of Sarcoidosis in Korea (유육종증 전국실태조사)

  • 대한결핵 및 호흡기학회 학술위원회
    • Tuberculosis and Respiratory Diseases
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    • v.39 no.6
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    • pp.453-473
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    • 1992
  • Background: National survey was performed to estimate the incidence of sarcoidosis in Korea. The clinical data of confirmed cases were analysed for the practice of primary care physicians and pulmonary specialists. Methods: The period of study was from January 1991 to December 1992. Data were retrospectively collected by correspondence with physicians in departments of internal medicine, dermatology, ophthalmology and neurology of the hospitals having more than 100 beds using returning postcards. In confirmed and suspicious cases of sardoidosis, case record chart for clinical and laboratory findings were obtained in detail. Results: 1) Postcards were sent to 523 departments in 213 hospitals. Internal medicine composed 41%, dermatology 20%, ophthalmology 20% and neurology 19%. 2) Postcards were returned from 241 departments (replying rates was 48%). 3) There were 113 confirmed cases from 50 departments and 10 cases. The cases were composed from internal medicine (81%), dermatology (13%), ophthalmology (3%) and neurology (3%). 78 confirmed cases were analysed, which were composed from department of internal medicine (92%), dermatology (5%), and neurology (3%). 4) The time span for analysed cases was 1980 to 1992. one case was analysed in 1980 and the number gradually increased to 18 cases in 1991. 5) The majority of patients (84.4%) were in the age group of 20 to 49 years. 6) The ratio of male to female was 1 : 1.5. 7) The most common chief complains were respiratory symptoms, dermatologic symptoms, generalized discomforts, visual changes, arthralgia, abdominal pains, and swallowing difficulties in order. 16% of the patients were asymptomatic. 8) Mean duration between symptom onset and diagnosis was 2 months. 9) The most common symptoms were respiratory, general, dermatologic, ophthalmologic, neurologic and cardiac origin in order. 10) Hemoglobin, hematocrits and platelet were in normal range. 58% of the patients had lymphopenia measuring less than 30% of white cell count. The ratio of CD4 to CD8 lymphocytes was $1.73{\pm}1.16$ with range of 0.43 to 4.62. ESR was elevated in 43% of the cases. 11) Blood chemistry was normal in most cases. Serum angiotensin converting enzyme (S-ACE) was $66.8{\pm}58.6\;U/L$ with the range of 8.79 to 265 U /L. Proteinuria of more than 150 mg was found in 42. 9% of the patients. 12) Serum IgG was elevated in 43.5%, IgA in 45.5%, IgM in 59.1% and IgE in 46.7%. The levels of complement C3 and C4 were in the normal range. Anti-nuclear antibody was detected in 11% of the cases. Kweim test was performed in 3 cases, and in all cases the result was positive. 13) FVC was decreased in 17.3%, FEV1 in 11.5%, FEV1/FVC in 10%, TLC in 15.2%, and DLco in 64.7%. 14) PaO2 was decreased below 90 mmHg in 48.6% and PaCO2 was increased above 45 mmHg in 5.7%. 15) The percentage of macrophages in BAL fluid was $51.4{\pm}19.2%$, lymphocytes $44.4{\pm}21.1%$, and the ratio of CD4 to CD8 lymphocytes was $3.41{\pm}2.07$. 16) There was no difference in laboratory findings between male and female. 17) Hilar enlargement on chest PA was present in 87.9% (bilaterally in 78.8% and unilaterally in 9.1%). 18) According to Siltzbach's classification, stage 0 was 5%, stage 158.3%, stage 228.3%, and stage 38.3%. 19) Hilart enlargement on chest CT was present in 92.6% (bilaterally 76.4% and unilaterally in 16.2%). 20) HRCT was done in 16 cases. The most common findings were nodules, interlobular thickening, focal patchy infiltrations in order. Two cases was normal finding. 21) Other radiologic examinations showed bone change in one case and splenomegaly in two cases. 22) Gallium scan was done in 12 cases. Radioactivity was increased in hilar and mediastinal lymph nodes in 8 cases and in parenchyme in 2 cases. 23) The pathologic diagnosis was commonly performed by transbrochial lung biopsy (TBLB, 47.3%), skin and mediastinal lymph nodes biopsy (34.5%), peripheral lymph nodes biopsy (23.6%), open lung biopsy (18.2%) and bronchial biopsy in order. 24) The most common findings in pathology were non·caseating granuloma (100%), multi-nucleated giant cell (47.3%), hyalinized acellular scar (34.5%), reticulin fibrin network (20%), inclusion body (10.9%), necrosis (9.1%), and lymphangitic distribution of granuloma (1.8%) in order. Conclusion: Clinical, laboratory, radiologic and pathologic findings were summarized. This collected data will assist in finding a test for detection and staging of sarcoidosis in Korea in near future.

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Estimation of GARCH Models and Performance Analysis of Volatility Trading System using Support Vector Regression (Support Vector Regression을 이용한 GARCH 모형의 추정과 투자전략의 성과분석)

  • Kim, Sun Woong;Choi, Heung Sik
    • Journal of Intelligence and Information Systems
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    • v.23 no.2
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    • pp.107-122
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    • 2017
  • Volatility in the stock market returns is a measure of investment risk. It plays a central role in portfolio optimization, asset pricing and risk management as well as most theoretical financial models. Engle(1982) presented a pioneering paper on the stock market volatility that explains the time-variant characteristics embedded in the stock market return volatility. His model, Autoregressive Conditional Heteroscedasticity (ARCH), was generalized by Bollerslev(1986) as GARCH models. Empirical studies have shown that GARCH models describes well the fat-tailed return distributions and volatility clustering phenomenon appearing in stock prices. The parameters of the GARCH models are generally estimated by the maximum likelihood estimation (MLE) based on the standard normal density. But, since 1987 Black Monday, the stock market prices have become very complex and shown a lot of noisy terms. Recent studies start to apply artificial intelligent approach in estimating the GARCH parameters as a substitute for the MLE. The paper presents SVR-based GARCH process and compares with MLE-based GARCH process to estimate the parameters of GARCH models which are known to well forecast stock market volatility. Kernel functions used in SVR estimation process are linear, polynomial and radial. We analyzed the suggested models with KOSPI 200 Index. This index is constituted by 200 blue chip stocks listed in the Korea Exchange. We sampled KOSPI 200 daily closing values from 2010 to 2015. Sample observations are 1487 days. We used 1187 days to train the suggested GARCH models and the remaining 300 days were used as testing data. First, symmetric and asymmetric GARCH models are estimated by MLE. We forecasted KOSPI 200 Index return volatility and the statistical metric MSE shows better results for the asymmetric GARCH models such as E-GARCH or GJR-GARCH. This is consistent with the documented non-normal return distribution characteristics with fat-tail and leptokurtosis. Compared with MLE estimation process, SVR-based GARCH models outperform the MLE methodology in KOSPI 200 Index return volatility forecasting. Polynomial kernel function shows exceptionally lower forecasting accuracy. We suggested Intelligent Volatility Trading System (IVTS) that utilizes the forecasted volatility results. IVTS entry rules are as follows. If forecasted tomorrow volatility will increase then buy volatility today. If forecasted tomorrow volatility will decrease then sell volatility today. If forecasted volatility direction does not change we hold the existing buy or sell positions. IVTS is assumed to buy and sell historical volatility values. This is somewhat unreal because we cannot trade historical volatility values themselves. But our simulation results are meaningful since the Korea Exchange introduced volatility futures contract that traders can trade since November 2014. The trading systems with SVR-based GARCH models show higher returns than MLE-based GARCH in the testing period. And trading profitable percentages of MLE-based GARCH IVTS models range from 47.5% to 50.0%, trading profitable percentages of SVR-based GARCH IVTS models range from 51.8% to 59.7%. MLE-based symmetric S-GARCH shows +150.2% return and SVR-based symmetric S-GARCH shows +526.4% return. MLE-based asymmetric E-GARCH shows -72% return and SVR-based asymmetric E-GARCH shows +245.6% return. MLE-based asymmetric GJR-GARCH shows -98.7% return and SVR-based asymmetric GJR-GARCH shows +126.3% return. Linear kernel function shows higher trading returns than radial kernel function. Best performance of SVR-based IVTS is +526.4% and that of MLE-based IVTS is +150.2%. SVR-based GARCH IVTS shows higher trading frequency. This study has some limitations. Our models are solely based on SVR. Other artificial intelligence models are needed to search for better performance. We do not consider costs incurred in the trading process including brokerage commissions and slippage costs. IVTS trading performance is unreal since we use historical volatility values as trading objects. The exact forecasting of stock market volatility is essential in the real trading as well as asset pricing models. Further studies on other machine learning-based GARCH models can give better information for the stock market investors.