<p>Actuarial science regards non-life insurance pricing as paradoxical, necessitating various algorithms to assess the risks. Auto insurance, in particular, requires precise models to predict the frequency <i>N</i> and amount <i>S</i> of claims in order to set adequate premiums and manage risks effectively. This framework analyzes the frequency and amount claims as well as integrates machine learning algorithms with Extreme Gradient Boosting regression to create a new approach which is powerful for zero-inflated data. Under specific hypothesis, we prove that the marginal probability distribution of <i>S</i> follows an infinite mixture of Gamma distributions, whereas the marginal probability distribution of <i>N</i> follows a Negative Binomial one. Simulation studies with perturbed data were carried out to evaluate the asymptotic properties of the obtained estimators which is based on the developed Expectation-Maximization algorithm. Moreover, under some conditions, the concavity of the conditional expected log-likelihood function is constituted with the maximization step of the Expectation-Maximization algorithm. We illustrate the application of the proposed model with an auto insurance claim real data. The results show that the new approach outperforms to other state-of-the-art models.</p>