Penalized estimators for modified Log-Bilal regression: simulations and applications

The Log-Bilal regression is survival regression model accounts for unique features of lifetime data. In this study, we modify the Log-Bilal distribution to enhance it flexibility, resulting in a model that exhibits an increasing, non-constant failure rate over time. To address the multicollinearity for the modified Log-Bilal regression, we introduce two penalized estimators: Ridge modified Log-Bilal (RidgeMBE) and Liu_type modified Log-Bilal (liuMBE) estimators. The properties for the suggested estimators are discussed and the superiority for the estimators were checked. The Liu-type estimator demonstrates superiority over the other estimators. A simulation study is conducted across various factors, which reveals that the Liu_type estimator outperforms the others in many cases. The proposed estimators were applied to real lifetime data from mechanical pumps which it gives the results confirming the results of the simulation study.