Deep Neural Distributional Regression for Reliability Modeling Using the Power Lindley Distribution

Accurate probabilistic prediction and uncertainty quantification are important in reliability engineering, survival analysis, predictive maintenance, healthcare, and risk assessment. This study proposes a deep neural distributional regression framework based on the Power Lindley distribution for modeling positive continuous and right‐censored outcomes. The framework models the distributional parameters as nonlinear functions of explanatory variables, thereby producing observation‐specific conditional distributions rather than only point predictions. Model estimation is performed through a censoring‐aware likelihood in which observed events contribute through the probability density function and right‐censored observations through the survival function. A systematic hyperparameter search and early stopping are used to improve optimization stability and generalization. The proposed method is evaluated through Monte Carlo simulations under nonlinear data‐generating mechanisms and an additional distributional misspecification scenario, and is further assessed using the Veterans′ Administration Lung Cancer and primary biliary cirrhosis benchmark datasets. Comparisons with linear regression, generalized linear models, random forest regression, and optimized deep neural regression demonstrate competitive predictive performance while preserving the principal advantage of direct probabilistic modeling. The framework provides individualized prediction intervals, conditional quantiles, survival probabilities, and other uncertainty measures. Additional interpretability analysis illustrates how explanatory variables influence the estimated distributional parameters. Overall, the proposed approach provides a flexible and interpretable framework for probabilistic prediction and uncertainty‐aware decision making in reliability and survival applications.