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 high relevance in the insurance literature. This type of data often exhibits positive skewness and heavy tails. In this work, we propose a new quantile regression model based on the scale-mixture Birnbaum-Saunders distribution for modeling personal accident insurance data. The maximum likelihood estimates of the model parameters are obtained via the EM algorithm. Two Monte Carlo simulation studies are performed using the R software. The first study aims to analyze the performances of the EM algorithm to obtain the maximum likelihood estimates, and the randomized quantile and generalized Cox-Snell residuals. In the second simulation study, the size and power of the Wald, likelihood ratio, score and gradient tests are evaluated. The two simulation studies are conducted considering different quantiles of interest and sample sizes. Finally, a real insurance data set is analyzed to illustrate the proposed approach.