A log-Birnbaum-Saunders Regression Model with Asymmetric Errors

TL;DR

This paper introduces a skewed log-Birnbaum-Saunders regression model based on the skewed sinh-normal distribution, providing new tools for modeling asymmetric data with influence diagnostics and demonstrating its practical usefulness.

Contribution

It presents a novel skewed log-Birnbaum-Saunders regression model with influence measures and applies it to real data, extending existing distribution models.

Findings

Model effectively captures asymmetric data.

Influence diagnostics help identify influential observations.

Application demonstrates practical usefulness.

Abstract

The paper by Leiva et al. (2010) introduced a skewed version of the sinh-normal distribution, discussed some of its properties and characterized an extension of the Birnbaum-Saunders distribution associated with this distribution. In this paper, we introduce a skewed log-Birnbaum-Saunders regression model based on the skewed sinh-normal distribution. Some influence methods, such as the local influence and generalized leverage are presented. Additionally, we derived the normal curvatures of local influence under some perturbation schemes. An empirical application to a real data set is presented in order to illustrate the usefulness of the proposed model.