Scale-mixture Birnbaum-Saunders quantile regression models applied to personal accident insurance data

The modeling of personal accident insurance data has been a topic of extreme relevance in the insurance literature. In general, the data often exhibit positive asymmetry and heavy tails and non-quantile Birnbaum-Saunders regression models have been used in the modeling strategy. In this work, we propose a new quantile regression model based on the scale-mixture Birnbaum-Saunders distribution, which is reparametrized by inserting a quantile parameter. The maximum likelihood estimates of the model parameters are obtained via the EM algorithm. Two Monte Carlo simulation studies were performed using the \texttt{R} software. The first study aims to analyze the performance of the maximum likelihood estimates, the information criteria AIC, AICc, BIC, HIC, the root of the mean square error, and the randomized quantile and generalized Cox-Snell residuals. In the second simulation study, the size and power of the the Wald, likelihood ratio, score and gradient tests are evaluated. The two simulation studies were conducted considering different quantiles of interest and sample sizes. Finally, a real insurance data set is analyzed to illustrate the proposed approach.