A More General Robust Loss Function

We present a loss function which can be viewed as a generalization of many popular loss functions used in robust statistics: the Cauchy/Lorentzian, 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 loss, and document several of its useful properties.