Generalized XGBoost Method

This method has achieved excellent predictive performance in many fields and has exhibited many advantages, and is consequently considered especially suitable for the statistical analysis of big data. However, this method is limited because its loss function must be convex. For many scenario-specific problems, such as non-life insurance pricing, the distribution of predictor variables is often heavytailed, so the optimal prediction performance may not be obtained by setting convex loss functions. Simultaneously, it is important to estimate the probability distribution of predictor variables. When the set parametric probability distribution contains more than two parameters, it may be necessary to model multiple parameters to obtain better prediction performance. Therefore, a more generalized regularized tree boosting method is required to make the loss function not limited to the convex function while modelling the tree boosting for multiple parameters, to adapt to the most common parametric probability distributions.