Comparison of Parameter Estimation Methods in A Kappa Distribution

- Journal title : Communications for Statistical Applications and Methods
- Volume 12, Issue 2, 2005, pp.285-294
- Publisher : The Korean Statistical Society
- DOI : 10.5351/CKSS.2005.12.2.285

Title & Authors

Comparison of Parameter Estimation Methods in A Kappa Distribution

Park Jeong-Soo; Hwang Young-A;

Park Jeong-Soo; Hwang Young-A;

Abstract

This paper deals with the comparison of parameter estimation methods in a 3-parameter Kappa distribution which is sometimes used in flood frequency analysis. Method of moment estimation(MME), L-moment estimation(L-ME), and maximum likelihood estimation(MLE) are applied to estimate three parameters. The performance of these methods are compared by Monte-carlo simulations. Especially for computing MME and L-ME, three dimensional nonlinear equations are simplified to one dimensional equation which is calculated by the Newton-Raphson iteration under constraint. Based on the criterion of the mean squared error, L-ME (or MME) is recommended to use for small sample size( n100) while MLE is good for large sample size.

Keywords

method of moment estimation;L-moment estimation;maximum likelihood estimation;equivariance;quantile estimation;simulation;

Language

Korean

References

1.

오은선(2001), Kappa 분포의 모수추정과 강수 자료에의 적용, 전남대학교 통계학과 석사학위논문

2.

황영아(2003), 3모수 카파분포의 모수추정 방법들의 비교, 전남대학교 통계학과 석사학위 논문

3.

Dupuis D.J. and Winchester, C.(2001), More on the four-parameter Kappa Distribution, Journal of Statistical Computation and Simulation, 71, 91-113

4.

Greenwood J.A., Landwehr P.W., Matalas N.C., and Wallis J.R.(1979), Probability weighted moments: Definition and relation to parameters of several distributions expressed in inverse form, Water Resources Research, 15, 1049-1064

5.

Hosking J.R.M.(1990), L-Moments: Analysis and Estimation of Distributions using Linear Combinations of Order Statistics, Jour. Royal Stat. Soc., B, 52, 105-124

6.

Hosking, J.R.M.(1994), The four parameter Kappa distribution, IBM Journal of Research & Development, 38, 251-258

7.

Hosking, J.R.M.(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

8.

Hosking, J.R.M., and Wallis, J.R.(1997). Regional Frequency Analysis: An Approach based on L-moments. Cambridge University Press, Cambridge

9.

Lehmann, E.L.(1983), Theory of Point Estimation, John Wiley and Sons, New York

10.

Mason, S.J., Waylen, P.R., Mimmack, G.M. et.al.(1999), Changes in extreme rainfall events in South Africa, Climatic Change, 41, 249-257

11.

Mielke, P.W.(1973), Another Family of Distributions for Describing and Analyzing Precipitation Data, Journal of Applied Meteorology 12, 275-280, 1973

12.

Mielke, P.W. and Johnson, E.S.(1973), Three-Parameter Kappa Distribution Maximum Liklihood Estimates and Likelihood Ratio Tests, Monthly Weather Review, 101, 701-707

13.

Mielke, P.W. and Johnson E.S.(1974), Some generalized Beta distributions of the second kind having desirable application features in hydrology and meteorology, Water Resource Research, 10, 223-226

14.

Park, J.S, and Jung, H.S.(2001), Modelling Korean extreme rainfall using a Kappa distribution and maxrmum likelihood estimates, Theoretical and Applied Climatology, 72, 55-64

15.

Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P.(1992), Numerical Recipes In Fortran 77, Second Edition, Cambridge University Press