A penalized likelihood approach to model the annual maximum flow with small sample sizes
DOI:
https://doi.org/10.11113/mjfas.v0n0.620Keywords:
Generalized extreme value, Penalized likelihood, Extreme value theory, Small sample sizeAbstract
The aim of this study is to model the annual maximum flow of several sites in Sabah with small sample sizes using the generalized extreme value (GEV) distribution. Previous studies have shown that the standard method of maximum likelihood estimates would give a poor estimation of the GEV parameters and quantiles for small data set. This study will consider the penalized likelihood estimates as an alternative method to improve the inference over the standard method and retains the modeling flexibility. As comparisons, we will illustrate the results of both methods to model the annual maximum flow in Sabah. The results show the implementation of the penalty function had the same effect to the GEV parameter estimates as suggested by previous studies.
References
Castillo, E., Hadi, A. S., Balakrishnan, N., Sarabia, J. M. 2005. Extreme Value and Related Models with Applications in Engineering and Science. New Jersey: Wiley.
Coles, S. G., 2001. An Introduction to Statistical Modeling of Extreme Values. Wiley, Hoboken: Springer.
Coles, S. G., Dixon, M. J. 1999. Likelihood based inference for extreme value models. Extremes, 2(1), 5-23.
Embrechts, P., Klüppelberg, C., Mikosch, T. 1997. Modelling Extremal Events for Insurance and Finance. Berlin: Springer Verlag.
Hosking, J. R. M., Wallis, J. R., Wood, E. F. 1985. Estimation of the generalized extreme value distribution by the method of probability weighted moments. Technometrics, 27, 251-261.
Martins, E. S., Stedinger, J. R. 2000. Generalized maximum likelihood generalized extreme value quantile estimators for hydrologic data. Water Resources Research, 36(3), 737-744.
Nadarajah, S., Choi, D. 2007. Maximum daily rainfall in South Korea. Journal of Earth System Science, 116(4), 311-320.
Nadarajah, S., Shiau, J. T. 2005. Analysis of extreme flood events for the Pachang River, Taiwan. Water Resource Management, 9(4), 363–374.
Phien, H. N., Fang, T. S. E. 1989. Maximum likelihood estimation of the parameters and quantiles of the general extreme value distribution from censored samples. Journal of Hydrology, 105, 139-155.
Smith, R. L., 1985. Maximum likelihood estimation in a class of non-regular cases. Biometrika, 72, 67–92.
Soukissian, T., Tsalis, C. 2015. The effect of the generalized extreme value distribution parameter estimation methods in extreme wind speed prediction. Journal of the International Society for the Prevention and Mitigation of Natural Hazards, 78(3), 1777-1809.
Zheng, W., Zhang, J., Liu, H., Li, J. 2014. A penalized maximum likelihood approach for m-year precipitation return values estimation with lattice spatial data. IEEE/CIC International Conference on Communications in China - Workshops (CIC/ICCC). 13 October 2014. Shanghai: IEEE, 16-20.
