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

Nathalia L. Chaves, Caio L. N. Azevedo, Filidor Vilca-Labra, Juvêncio S. Nobre

In this paper we introduce a new distribution for positive and skewed data by combining the Birnbaum-Saunders (BS) distribution and the centred skew-normal distribution. Several of its properties are developed. Our model accommodates both positively and negatively skewed positive data. Also, we show that our model circumvents some problems related to another BS distribution, based on the skew-normal distribution under the direct parameterization, previously presented in the literature. We developed both maximum likelihood (ML) and Bayesian estimation procedures, comparing them through a suitable simulation study. The convergence of the expectation conditional maximization (ECM) (for ML inference) and MCMC algorithms (for Bayesian inference) were veri ed and several factors of interest were compared in the parameter recovery study. In general, as the sample size increases, the results indicated that the Bayesian approach provided the most accurate estimates. Finally, our model accommodates the asymmetry of the data, compared with the usual BS model, which is illustrated through real data analysis.