• Title/Summary/Keyword: Statistical distributions

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Statistical Analysis on Microcrack Length Distribution in Tertiary Crystalline Tuff (제3기 결정질 응회암에서 발달하는 미세균열의 길이 분포에 대한 통계적 분석)

  • Park, Deok-Won
    • The Journal of the Petrological Society of Korea
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    • v.20 no.1
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    • pp.23-37
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    • 2011
  • The scaling properties on the length distribution of microcrack populations from Tertiary crystalline tuff are investigated. From the distribution charts showing length range with 15 directional angles and five groups(I~V), a systematic variation appears in the mean length with microcrack orientation. The distribution charts are distinguished by the bilaterally symmetrical pattern to nearly N-S direction. The whole domain of the length-cumulative frequency diagram for microcrack populations can be divided into three sections in terms of phases of the distribution of related curves. Especially, the linear middle section of each diagram of five groups represents a power-law distribution. The frequency ratio of linear middle sections of five groups ranges from 46.6% to 67.8%. Meanwhile, the slope of linear middle section of each group shows the order: group V($N60{\sim}90^{\circ}E$, -2.02) > group IV($N20{\sim}60^{\circ}E$, -1.55) > group I($N60{\sim}90^{\circ}W$, -1.48), group II($N10{\sim}60^{\circ}W$, -1.48) > group III($N10^{\circ}W{\sim}N20^{\circ}E$, -1.06). Five sub-populations(five groups) that closely follow the power-law length distribution show a wide range in exponents( -1.06 - -2.02). These differences in exponent among live groups emphasizes the importance of orientation effect. In addition, breaks in slope in the lower parts of the related curves represent the abrupt development of longer lengths, which is reflected in the decrease in the power-law exponent. Especially, such a distribution pattern can be seen from the diagram with $N10{\sim}20^{\circ}E,\;N10{\sim}20^{\circ}W$ and $N60{\sim}70^{\circ}W$ directional angles. These three directional angles correspond with main directions of faults developed around the study area. The distribution chart showing the individual characteristics of the length-cumulative frequency diagrams for 15 directional angles were made. By arraying above diagrams according to the categories of three groups(A, B and C), the differences in length-frequency distributions among these groups can be easily derived. The distribution chart illustrates the importance of analysing microcrack sets separately. From the related chart, the occurrence frequency of shorter microcracks shows the order: group A > group B > group C. These three types of distribution patterns could reveal important information on the processes occurred during microcrack growth.

Geographical Characteristics of PM2.5, PM10 and O3 Concentrations Measured at the Air Quality Monitoring Systems in the Seoul Metropolitan Area (수도권 지역 도시대기측정소 PM2.5, PM10, O3 농도의 지리적 분포 특성)

  • Kang, Jung-Eun;Mun, Da-Som;Kim, Jae-Jin;Choi, Jin-Young;Lee, Jae-Bum;Lee, Dae-Gyun
    • Korean Journal of Remote Sensing
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    • v.37 no.3
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    • pp.657-664
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    • 2021
  • In this study, we investigated the relationships between the air quality (PM2.5, PM10, O3) concentrations and local geographical characteristics (terrain heights, building area ratios, population density in 9 km × 9 km gridded subareas) in the Seoul metropolitan area. To analyze the terrain heights and building area ratios, we used the geographic information system data provided by the NGII (National Geographic Information Institute). Also, we used the administrative districts and population provided by KOSIS (Korean Statistical Information Service) to estimate population densities. We analyzed the PM2.5, PM10, and O3 concentrations measured at the 146 AQMSs (air quality monitoring system) within the Seoul metropolitan area. The analysis period is from January 2010 to December 2020, and the monthly concentrations were calculated by averaging the hourly concentrations. The terrain is high in the northern and eastern parts of Gyeonggi-do and low near the west coastline. The distributions of building area ratios and population densities were similar to each other. During the analysis period, the monthly PM2.5 and PM10 concentrations at 146 AQMSs were high from January to March. The O3 concentrations were high from April to June. The population densities were negatively correlated with PM2.5, PM10, and O3 concentrations (weakly with PM2.5 and PM10 but strongly with O3). On the other hand, the AQMS heights showed no significant correlation with the pollutant concentrations, implying that further studies on the relationship between terrain heights and pollutant concentrations should be accompanied.

Effect of Dietary Streptococcus faecium on the Performances and the Changes of Intestinal Microflora of Broiler Chicks (Streptococcus faecium의 급여가 육계의 성장과 장내 세균총 변화에 미치는 영향)

  • Kim, K.S.;Chee, K.M.;Lee, S.J.;Cho, S.K.;Kim, S.S.;Lee, W.
    • Korean Journal of Poultry Science
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    • v.18 no.2
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    • pp.97-119
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    • 1991
  • Effect of Streptococcus faecium(SF) and an antibiotic, Colistin(Col), supplemented to diets singly or in combination, on the performances and changes of intestinal population of microflora of broiler chicks studied. A total of 252, day-old chicks(Arbor Acre) of mixed sex(M:F=1:1) were alloted into six groups. A diet with no Col and SF was referred as a control diet. The basal diets were added with two levels of SF, 0.04 and 0.08%, singly or in combination with Col 10ppm Another diet was prepared by adding only Col 10 ppm. Numbers of the microorganism in diets added with SF 0.04% and 0.08% were 7$\times$10$^{4}$ and 1.4$\times$10$^{5}$ /g diet respectively The diets consisting of corn and soybean meal as major ingredients were fed for a period of seven weeks . During the feeding trial, fresh excreta were sampled at the end of every week in a sterilized condition to count microbial changes from each dietary group. Microbial changes of large intestine were also measured from nine birds sacrificed at the end of the 4th and 7th weeks each time per dietary group. Excreta from all the groups were also collected quantitatively at the end of 3rd and 6th weeks to measure digestibility of the diets, At the end of 7th week, nine birds from each group were also sacrificed to measure weight changes of gastrointestinal tracts . Average body weight gains of broilers fed the diets added with SF 0.08% (2.37kg) or SF 0. 08%+col 10ppm(2.34kg) were significantly larger than that of the control(2.18kg). The weight gains of the other groups were not statistically different from that of the control Feed/gain ratios of the supplemental groups were better than that of control (P<0.05) except that of birds fed the diet added only with SF 0.04%. Digestibilities of nutrients such as dry matter, crude protein, crude fat and total carbohydrates were not altered by the consumption of the diets added with SF and/or Col throughout the whole feeding period. As expected, the numbers of Streptococci in the excreta from birds fed diets added with SF increased significantly with a statistical difference between groups with SF 0.04% and SF 0.08% most of the time. However. addition of Colistin to the diets supplemented with SF did not give any effects on the number of the microorganism. Numbers of coliforms in the excreta were apparently reduced by feeding the diets added with SF and/or Col(P<0.05). There were, however, no additive effects observed between the two feed additives in this regard when supplementing Col to the SF diets. Distributions of intestinal microflora exhibited exactly the same pattern as those of the excreta. Length of small intestine of the birds fed diets added with SF 0.08% with or without Col 10 ppm became significantly longer with a range of about 10% than those of the birds fed diets without SF. However, the empty weight of the small inestine of the former group was lighter than that of control These changes resulted in a significant reduction in weight/unit length of the intestine of the birds fed diets supplemented with Col and SF singly or in combination. In overall conclusion, diet added with SF 0.08% appeared most effective in improving broiler performances. Colistin added at a level of 10ppm was not beneficial at all in itself or in combination with SF in terms of broiler performances or changes of intestinal microflora population. The efficacy of SF and Col could be attributed to the changes of wall thickness of the small intestine.

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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.