Given an ordered sample of either exceedances or upper order statistics which is to be modeled using a GPD with
distribution function \(F\), this function provides Segers' estimator of the shape parameter \(\gamma\),
see Segers (2005). Precisely, for \(k = \{1, \ldots, n-1\}\), the estimator can be written as
$$\hat \gamma^k_{\rm{Segers}}(H) = \sum_{j=1}^k \Bigl(\lambda(j/k) - \lambda((j-1)/k)\Bigr) \log \Bigl(H^{-1}((n-\lfloor cj \rfloor)/n)-H^{-1}((n-j)/n) \Bigr)$$
for \(H\) either the empirical or the distribution function based on the log--concave density estimator
and \(\lambda\) the mixing measure given in Segers (2005), Theorem 4.1, (i).
Note that for any \(k\), \(\hat \gamma^k_{\rm{Segers}} : R^n \to (-\infty, \infty)\).
If \(\hat \gamma_{\rm{Segers}} \not \in [-1,0)\), then it is likely that the log-concavity assumption is violated.