The mean of the GPD distribution is $ \mu +{ \frac {\lambda }{1-\xi }}\,\;$, always for $(\xi <1) $. I tried to solve this integral but it did not seem clear to find the result given. Can someone help me? $$\mathop{\mathbb{E}}(X) = \mu= \int_{-\infty}^{\infty} x f(x) \, {\rm d}x$$ $$\int_{-\infty}^{\infty} x f(x) \, {\rm d}x = \int_{-\infty}^{\infty} x \frac 1\lambda(1+\frac \xi\lambda(x-m))^{-(1+ \frac 1 \xi)} \, {\rm d}x $$
2026-04-13 02:40:08.1776048008
How to calculate the mean of the Generalized Pareto Distribution?
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