Zero-adjusted Birnbaum-Saunders regression model

In this paper we introduce the zero-adjusted Birnbaum-Saunders regression model. This new model generalizes at least seven Birnbaum-Saunders regression models. The idea of this modeling is mixing a degenerate distribution at zero with a Birnbaum-Saunders distribution. Besides the capacity to account for excess zeros, the zero-adjusted Birnbaum-Saunders distribution additionally produces an attractive modeling structure to right-skewed data. In this model, the mean and precision parameter of the Birnbaum-Saunders distribution and the probability of zeros can be related to linear and/or non-linear predictors through link functions. We derive a type of residual to perform diagnostic analysis and a perturbation scheme for identifying those observations that exert unusual influence on the estimation process. Finally, two applications to real data show the potential of the model.

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