Publisher : Korean Data and Information Science Society
DOI : 10.7465/jkdi.2016.27.4.1001
Title & Authors
The estimation of CO concentration in Daegu-Gyeongbuk area using GEV distribution Ryu, Soorack; Eom, Eunjin; Kwon, Taeyong; Yoon, Sanghoo;
It is well known that air pollutants exert a bad influence on human health. According to the United Nations Environment Program, 4.3 million people die from carbon monoxide and particulate matter annually from all over the world. Carbon monoxide is a toxic gas that is the most dangerous of the gas consisting of carbon and oxygen. In this paper, we used 1 hour, 6 hours, 12 hours, and 24 hours average carbon monoxide concentration data collected between 2004 and 2013 in Daegu Gyeongbuk area. Parameters of the generalized extreme value distribution were estimated by maximum likelihood estimation and L-moments estimation. An evalution of goodness of fitness also was performed. Since the number of samples were small, L-moment estimation turned out to be suitable for parameter estimation. We also calculated 5 year, 10 year, 20 year, and 40 year return level.
Carbon monoxide;generalized extreme value distribution;l-moments;MLE;return level;
Anderson, T. W. and Darling, D. A. (1952). Asymptotic theory of certain "Goodness of Fit" criteria based on stochastic processes. Annals of Mathematical Statistics, 23, 193-212.
Fisher, R. A. and Tippett, L. H. C. (1928). Limiting forms of the frequency distribution of the largest or smallest member of a sample. Mathematical Proceedings of the Cambridge Philosophical Society, 24, 180-190.
Gnedenko, B. V. (1943). Sur la distribution limite du terme maximum d'une serie aleatoire. Annals of Mathematics, 44, 423-453.
Greenwood, J. A., Landwehr, J. M., Matalas, N. C. and Wallis, J. R. (1979). Probability weighted moments: Definition and relation to parameters of several distributions expressable in inverse form. Water Resources Research, 15, 1049-1054.
Hosking, J. R. M., Wallis, J. R. and Wood, E. F. (1985). Estimation of the generalised extreme value distribution by the method of probability weighted monents. Technometrics, 27, 251-261.
Hosking, J. R. M. and Wallis, J. R. (1987). Parameter and quantile estimation for the generalized Pareto distribution. Technometrics, 29, 339-349.
Hosking, J. R. M. (1990). L-moments: Analysis and estimation of distributions using linear combinations of order statistics. Journal of the Royal Statistical Society B, 52, 105-124.
Jenkinson, A. F. (1955). The frequency distribution of the annual maximum (or minimum) values of meteorological elements. Quarterly Journal of the Royal Meteorological Society, 81, 158-171.
Kim, H. D. and Kim, H. T. (2015). Finding optimal portfolio based on genetic algorithm with generalized Pareto distribution. Journal of the Korean Data & Information Science Society, 26, 1479-1494.
Kim, J. C., Park, C, R. and Kim, S. H. (2015). On the extreme value distribution of foreign exchange rates using L-moments. The Korean Journal Of Financial Engineering, 14, 1-33.
Kim, Y. K. (2015). A hierarchical bayesian modeling of temporal trends in return levels for extreme precipitations. The Korean Journal of Applied Statistics, 28, 137-149.
Koh, D. K., Choo, T. H., Maeng, S. J. and Trivedi, C. (2008). Regional frequency analysis for rainfall using L-moment. The Journal of the Korea Contents Association, 8, 252-263.
Longin, F. M. (1996). The asymptotic distribution of extreme stock market returns. Journal of Business, 69, 383-408.
Longin, F. M. (2000). From value at risk to stress testing: The extreme value approach. Journal of Banking and Finance, 24, 1097-1130.
Prescott, P. and Walden, A. T. (1980). Maximum likeihood estimation of the parameters of the generalized extreme value distribution. Biometrika, 67, 723-724.
Shin, H. J., Sung, K. M. and Heo, J. H. (2010). Derivation of modified anderson-darling test statistics and power test for the gumbel distribution. Journal of Korea Water Resources Association, 43, 813-822.
Sohn, K. T. and Liang, X. (2014). Estimation of return levels of typhoon best track data based on generalized extreme value distribution. Journal of the Korean Data Analysis Society, 16, 1259-1267.
Smirnov, N. V. (1939). On the estimation of the discrepancy between empirical curves of distribution for two independent samples. Bulletin of Mathematical University of Moscow, 2, 3-16.
Sung, Y. K. and Sohn, J. K. (2013). Prediction of extreme rainfall with a generalized extreme value distribution. Journal of theKorean Data & Information Science Society, 24, 857-865.