Advanced SearchSearch Tips
Wakeby Distribution and the Maximum Likelihood Estimation Algorithm in Which Probability Density Function Is Not Explicitly Expressed
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
Wakeby Distribution and the Maximum Likelihood Estimation Algorithm in Which Probability Density Function Is Not Explicitly Expressed
Park Jeong-Soo;
  PDF(new window)
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.
L-moment estimation;Numerical optimization;Hydrology;Quantile function;Newton-Raphson algorithm;
 Cited by
맹승진 (2000). '수문 자료의 통계학적 분석 방법', 한국수자원공사 연구 홈페이지에서 입수,

박정수, 황영아 (2005). 3-모수 카파분포에서 추정방법들의 비교, '한국통계학회논문집', 제12권 2호, 인쇄중

허준행 (1997). 수문통계학의 기초(5), '한국수자원학회지', 제30권 1호, 88-96

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

Hosking, JRM (2000). LMOMENTS: Fortran routines for use with the method of L-moments, Version 3.03, available at

Hosking, J.R.M., and Wallis, J.R., (997). Regional Frequency Analysis: An Approach based on L-moments. Cambridge University Press, Cambridge

Huh, M. Y. (1986). Computation of percentage points. Communications in Statistics-Simulation and Computation, Vol. 15, 1191-1198 crossref(new window)

Karian, Z., and Dudewicz, E.J. (2000). Fitting Statistical Distribution, CRC Press, Boca Raton, Florida

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 crossref(new window)

Landwehr JM, Matalas NC, and Wallis JR. (1980). Quantile estimation with more or less floodlike distributions. Water Resources Research. Vol. 16, 547-555 crossref(new window)

Lawrence CT, and Tits A. (2001). A computationally efficient feasible sequential quadratic programming algorithm. SIAM Journal of Optimization, Vol. 11(4), 1092-1118 crossref(new window)

Nocedal, J. and Wright, SJ. (1999). Numerical Optimization, Springer, New York

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 crossref(new window)