A Least Squares Estimation of a Hybrid log-Poisson Regression and its Goodness of Fit for Optimal Loss Reserves in Insurance

In this article, the parameters of a hybrid log-linear model (log-Poisson) are estimated using the fuzzy least-squares (FLS) procedures (Celmi\c{n}\v{s}, 987a,b, D'Urso and Gastaldi, 2000, DUrso and Gastaldi, 2001). A goodness of fit have been derived in order to assess and compare this new model and the classical log-Poisson regression in loss reserving framework (Mack, 1991). Both the hybrid model and its goodness of fit are performed on a loss reserving data.