A More General Robust Loss Function

We present a two-parameter loss function which can be viewed as a generalization of many popular loss functions used in robust statistics: the Cauchy/Lorentzian, Geman-McClure, Welsch, and generalized Charbonnier loss functions(and by transitivity the L2, L1, L1-L2, and pseudo-Huber/Charbonnier loss functions). We describe and visualize this penalty, and document several of its useful properties.