Résumé
A general procedure for deriving statistical tests on the shape parameter
ξ of a generalized Pareto distribution (GPD)
G
ξ,
β
is proposed. From the existence condition of the GPD, statistics which discriminate between possible
ξ values can be derived by elimination of the
β parameter through a probability weighted moment (PWM) approach. The test statistics used are independent of the
β 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.