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A statistical test procedure for the shape parameter of a generalized Pareto distribution. (English) Zbl 1429.62066

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

MSC:

62F03 Parametric hypothesis testing
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