广义Pareto分布参数的最小二乘估计∗

摘要

传统的广义Pareto分布(Generalized Pareto Distribution,简记GPD)的参数估计一般受分布形状参数的约束。如：矩估计(the Method of Moments,简记MOM),概率加权矩估计(the Probability Weighted Moments,简记PWM), L矩估计(简记LM),极大似然估计(Maximum Likelihood Estima-tion,简记MLE)等。本文利用GDP可转化成指数分布的事实及指数分布参数估计的结果,利用最小二乘(the Least Squares,简记LS)法,得到了两参数和三参数GPD的参数估计；给出了估计量具有渐近正态性的结果。估计方法不受分布形状参数的限制。模拟显示：本文提出的估计在某些常用条件下优于GPD的其他参数估计,如MOM, PWM, LM,以及基于分位数估计(the Elemental Percentile Method,简记EPM)等。%Traditional estimations of parameters of the generalized Pareto distribution (GPD) are generally constrained by the shape parameter of GPD. Such as: the method-of-moments (MOM), the probability-weighted moments (PWM), L-moments (LM), the maximum likelihood estimation (MLE) and so on. In this paper we use the fact that GPD can be transformed into the exponential distribution and use the results of parameters estimation for the exponential distribution, than we propose parameters estimators of the two-parameter or three-parameter GPD by the least squares method. Some asymptotic results are provided and the proposed method not constrained by the shape parameter of GPD. A simulation study is carried out to evaluate the performance of the proposed method and to compare them with other methods suggested in this paper. The simulation results indicate that the proposed method performs better than others in some common situation.