A new distribution for robust least squares

Abstract

A new distribution is introduced, which we call the twin-t distribution. This distribution is heavy-tailed like the t distribution, but closer to normality in the central part of the curve. Its properties are described, e.g. the pdf, the distribution function, moments, and random number generation. This distribution could have many applications, but here we focus on its use as an aid to robustness. We give examples of its application in robust regression and in curve fitting. Extensions such as skew and multivariate twin-t distributions, and a twin of