广义Pareto分布近似广义最小二乘估计

Parameter Estimation of Approximated Generalized Least Squares Estimators for the Generalized Pareto Distribution

摘要: 广义Pareto分布(generalized Pareto distribution,GPD)是统计分析中的一个极为重要的分布.对基于广义Pareto分布的若干个样本分位数进行了研究.首先,求解具有较高精度的形状参数的参数估计;其次,得出广义Pareto分布位置参数及尺度参数的近似广义最小二乘估计.本方法简单易行,对形状参数的存在条件没有限制,通过Monte Carlo模拟验证了该方法具有较高的精度.

Abstract: The generalized Pareto distribution (GPD) is one of the most important distribution in statistics analysis.This paper is based on sample quantiles of the GPD.First,the shape parameter estimator that has high estimated precision is solved,then the approximated generalized least squares estimation expressions of the location and scale parameters are obtained for the GPD.The proposed method is easy and has no limitation for the shape parameter.In addition,it has high estimation accuracy under Monte-Carlo simulation tests.