A statistical test procedure for the shape parameter of a generalized Pareto distribution
A general procedure for deriving statistical tests on the shape parameter ? of a generalized Pareto distribution (GPD) G?,? is proposed. From the existence condition of the GPD, statistics which discriminate between possible ? values can be derived by elimination of the ? parameter through a probability weighted moment (PWM) approach. The test statistics used are independent of the ? value and related to the chosen PWM approach. Two particular statistics are considered and a simulation study shows how the proposed procedure outperforms the classical maximum likelihood ratio test for small sample sizes.
generalized pareto distribution probability weighted moment maximum likelihood ratio test small sample size