A new distribution for robust least squares

TL;DR

The paper introduces the twin-t distribution, a new heavy-tailed distribution closer to normality in the center, designed to improve robustness in statistical modeling and applications like regression and curve fitting.

Contribution

It presents the mathematical properties and potential applications of the twin-t distribution, a novel distribution combining heavy tails with central normality.

Findings

The twin-t distribution has desirable properties for robust statistical analysis.

It improves robustness in regression and curve fitting tasks.

Extensions to skewed and multivariate forms are discussed.

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