Tweedie regularization model and application

Abstract

This article proposes a new regular model called the Tweedie regular regression model. The Tweedie distributions are parameterized by their mean, dispersion and power parameter ξ. For each ξ, we obtain a specific regular model. Tweedie Regression model includes several distributions. In particular, for ξ = 0, we obtain the Gaussian case; the estimation of the parameters through the classical point of view has been done using Least Absolute Shrinkage and Selection Operator (Lasso), Ridge and Elastic methods. Therefore, the proposed model is appropriate for modeling equiover and underdispersed data. The parameters estimation, through the classical point of view, has been performed using the methods of Lasso, Ridge and Elastic approaches. The Tweedie regular regression model will be calibrated by choosing one of the Lasso, Ridge and Elastic approaches. To evaluate our suggested method, a detailed comparison study through a simulation and real data was conducted to verify the proposed models. It was carried out to examine the fitness of the estimated parameters. Compared with counterparts, the results demonstrate the superiority of models Ridge Tweedie Regression (RTR), Lasso Tweedie Regression (LTR), and Elastic Tweedie Regression (ETR) using MAE (Mean absolute error), RMSE (Root Mean Squared Error) and R-squared (Coefficient of determination)