Statistics and Its Interface

Volume 13 (2020)

Number 3

A log Birnbaum-Saunders regression model based on the skew-normal distribution under the centred parameterization

Pages: 335 – 346



Nathalia L. Chaves (Department of Statistics, State University of Campinas, SP, Brazil)

Caio L. N. Azevedo (Department of Statistics, State University of Campinas, SP, Brazil)

Filidor Vilca-Labra (Department of Statistics, State University of Campinas, SP, Brazil)

Juvêncio S. Nobre (Department of Statistics and Applied Mathematics, Federal University of Ceará, Brazil)


In this paper we introduce a new regression model for positive and skewed data, a log Birnbaum–Saunders model based on the centred skew-normal distribution, also presenting several inference tools for this model. Initially, we developed a new version of the skew-sinh-normal distribution, describing some of its properties. For the proposed regression model, we carry out, through the expectation conditional maximization (ECM) algorithm, parameter estimation, model fit assessment, model comparison and residual analysis. Finally, our model accommodates more suitably the asymmetry of the data, compared with the usual log Birnbaum–Saunders model, which is illustrated through a real data analysis.


Birnbaum-Saunders distribution, Skew-sinh-normal distribution, Frequentist inference, ECM algorithm

2010 Mathematics Subject Classification

62F10, 62J12, 62J20, 62P99

The authors would like to thank CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior) for the financial support through a Master Scholarship granted to the first author under the guidance of the second and also to Conselho Nacional Desenvolvimento Científico e Tecnológico for a research scholarship, grant number (308339/2015-0).

Received 27 April 2018

Accepted 24 January 2020

Published 22 April 2020