Generalized Pareto Distribution Parameter Estimation

Traditional estimations of parameters of the generalized Pareto distribution (GPD) are constrained by the shape parameter of GPD, generally. 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 pro-posed the estimator of the parameters of three-parameter GPD, based on the linear model at the first time. Some asymptotic results are provided, and proposed method is not constrained by the shape parameter of GPD. The proposed method performs better than others for 3-parameter GPD in some cases, by the results of simulations. In addition, in this paper we transform GPD into the exponential distribution and use the results of parameters estimation for the exponential distribution, than we propose parameters estimators for the two-parameter or three-parameter GPD by the least squares method. Some asymptotic results are also provided and the second method proposed is also not constrained by the shape parameter of GPD. A simu-lation study is carried out to evaluate the performance of the second 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.