Scale-mixture Birnbaum-Saunders quantile regression models applied to
personal accident insurance data
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abstract
The modeling of personal accident insurance data has been a topic of extreme
relevance in the insurance literature. This kind 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 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.
