A risk model for Forest fires based on asymptotic results for multivariate collective models. Single models and structured families of models

In this paper we propose an new approach to multivariate collective models based on asymptotic distibutions, since the modeling problems posed have large samples. Collective risk models play an important part in Risk Theory and in Actuarial Mathematics. Inference based on these models is centered on claims totals. However, the new approach has in mind a different kind of risk, the risk of forest fires, where the variables of interest are the number fires and the total burnt areas. As a result, a special case bivariate risk model is derived with this intent. Besides single models, structured families whose models correspond to the treatments of a base linear model are considered. This leads to an ANOVA-like situation where we don’t have to estimate the error, which enable to test the influence of several factors on the multivariate collective models mean vectors. Instead of F tests, we use χ2 tests, availing us of asymptotic distributions that lightens the treatment. To illustrate the approach, an application to forest fires in Portugal with real data is presented.