Parameter estimation of the generalized Pareto distribution-Part I

被引:120
作者
Bermudez, P. de Zea [1 ]
Kotz, Samuel [2 ]
机构
[1] Univ Lisbon, Fac Ciencias, Dept Estatist & Invest Operac, P-1749016 Lisbon, Portugal
[2] George Washington Univ, Dept Engn Management & Syst Engn, Sch Engn & Appl Sci, Washington, DC 20052 USA
关键词
Generalized Pareto distribution; Maximum likelihood; Method of moments; Probability weighted moments; Least squares; Order statistics; PROBABILITY WEIGHTED MOMENTS; STATISTICAL-INFERENCE; EXTREME QUANTILES; LH-MOMENTS; FREQUENCY;
D O I
10.1016/j.jspi.2008.11.019
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
The generalized Pareto distribution (GPD) has been widely used in the extreme value framework. The success of the GPD when applied to real data sets depends substantially on the parameter estimation process. Several methods exist in the literature for estimating the GPD parameters. Mostly, the estimation is performed by maximum likelihood (ML). Alternatively, the probability weighted moments (PWM) and the method of moments (MOM) are often used, especially when the sample sizes are small. Although these three approaches are the most common and quite useful in many situations, their extensive use is also due to the lack of knowledge about other estimation methods. Actually, many other methods, besides the ones mentioned above, exist in the extreme value and hydrological literatures and as such are not widely known to practitioners in other areas. This paper is the first one of two papers that aim to fill in this gap. We shall extensively review some of the methods used for estimating the GPD parameters, focusing on those that can be applied in practical situations in a quite simple and straightforward manner. (C) 2009 Elsevier B.V. All rights reserved.
引用
收藏
页码:1353 / 1373
页数:21
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