  The breakdown point in its different variants is one of the central notions
to quantify the global robustness of a procedure. We propose a simple
supplementary variant which is useful in situations where we have no obvious or
only partial equivariance: Extending the Donoho and Huber(1983) Finite Sample
Breakdown Point, we propose the Expected Finite Sample Breakdown Point to
produce less configuration-dependent values while still preserving the finite
sample aspect of the former definition. We apply this notion for joint
estimation of scale and shape (with only scale-equivariance available),
exemplified for generalized Pareto, generalized extreme value, Weibull, and
Gamma distributions. In these settings, we are interested in highly-robust,
easy-to-compute initial estimators; to this end we study Pickands-type and
Location-Dispersion-type estimators and compute their respective breakdown
points.
