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http://dx.doi.org/10.5351/CKSS.2005.12.2.443

Wakeby Distribution and the Maximum Likelihood Estimation Algorithm in Which Probability Density Function Is Not Explicitly Expressed  

Park Jeong-Soo (Department of Statistics, Chonnam National University)
Publication Information
Communications for Statistical Applications and Methods / v.12, no.2, 2005 , pp. 443-451 More about this Journal
Abstract
The studied in this paper is a new algorithm for searching the maximum likelihood estimate(MLE) in which probability density function is not explicitly expressed. Newton-Raphson's root-finding routine and a nonlinear numerical optimization algorithm with constraint (so-called feasible sequential quadratic programming) are used. This algorithm is applied to the Wakeby distribution which is importantly used in hydrology and water resource research for analysis of extreme rainfall. The performance comparison between maximum likelihood estimates and method of L-moment estimates (L-ME) is studied by Monte-carlo simulation. The recommended methods are L-ME for up to 300 observations and MLE for over the sample size, respectively. Methods for speeding up the algorithm and for computing variances of estimates are discussed.
Keywords
L-moment estimation; Numerical optimization; Hydrology; Quantile function; Newton-Raphson algorithm;
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1 Huh, M. Y. (1986). Computation of percentage points. Communications in Statistics-Simulation and Computation, Vol. 15, 1191-1198   DOI
2 맹승진 (2000). '수문 자료의 통계학적 분석 방법', 한국수자원공사 연구 홈페이지에서 입수, http://www.kowaco.or.kr/~water/water-dic/seawater/waterco16-4.html
3 박정수, 황영아 (2005). 3-모수 카파분포에서 추정방법들의 비교, '한국통계학회논문집', 제12권 2호, 인쇄중
4 허준행 (1997). 수문통계학의 기초(5), '한국수자원학회지', 제30권 1호, 88-96
5 Hosking JRM (1990). L-moments: analysis and estimation of distributions using linear combinations of order statistics. Journal of The Royal Statistical Society, Series B, Vol. 52(1), 105-124
6 Hosking, JRM (2000). LMOMENTS: Fortran routines for use with the method of L-moments, Version 3.03, available at http://www.research.ibm.com/people/h/hosking/lmoments.html
7 Hosking, J.R.M., and Wallis, J.R., (997). Regional Frequency Analysis: An Approach based on L-moments. Cambridge University Press, Cambridge
8 Karian, Z., and Dudewicz, E.J. (2000). Fitting Statistical Distribution, CRC Press, Boca Raton, Florida
9 Landwehr J.M., Matalas N.C., and Wallis J.R. (1979). Estimation of parameters and quantiles of Wakeby distributions. Water Resources Research, Vol. 15, 1361-1379   DOI
10 Landwehr JM, Matalas NC, and Wallis JR. (1980). Quantile estimation with more or less floodlike distributions. Water Resources Research. Vol. 16, 547-555   DOI   ScienceOn
11 Lawrence CT, and Tits A. (2001). A computationally efficient feasible sequential quadratic programming algorithm. SIAM Journal of Optimization, Vol. 11(4), 1092-1118   DOI   ScienceOn
12 Nocedal, J. and Wright, SJ. (1999). Numerical Optimization, Springer, New York
13 Park JS, lung HS, Kim RS, and Oh JH (2001). Modelling summer extreme rainfall over the Korean peninsula using Wakeby distribution. International Journal of Climatology, Vol. 21, 1371-1384   DOI   ScienceOn