Applied statistical modeling of infant mortality with the progressively censored IPMCJ distribution

Accurate estimation and modeling of infant mortality rates are essential for public health planning and medical research, as they are influenced by a wide range of biological, environmental, and socio-economic factors. To capture the underlying failure patterns, we proposed the inverse power–modified Chris–Jerry (IPMCJ) distribution, a generalized lifetime model particularly suited for decreasing failure rates. Progressive censoring (PC) was incorporated to address the common challenge of incomplete data collection in mortality studies. The statistical properties of the IPMCJ model were studied in detail, and parameter estimation was conducted through maximum likelihood and Bayesian approaches. Bayesian inference was further explored under symmetric squared error and asymmetric linear exponential (LINEX) loss functions, supported by confidence and credible intervals constructed via bootstrap, asymptotic, and Markov chain Monte Carlo (MCMC) methods. The practical relevance of the IPMCJ model was demonstrated using two real infant mortality datasets, where it consistently outperformed ten competing distributions. Convergence was evaluated using maximum likelihood checks and standard Bayesian diagnostics. Model performance of the IPMCJ distribution was validated using (a) the nonparametric Kaplan-Meier estimator and (b) comparisons with the complete-sample analysis. Extensive simulation studies confirmed the robustness and accuracy of the proposed estimators. The results emphasized the value of combining PC with the IPMCJ distribution, offering an effective framework for analyzing infant mortality data and informing health policy decisions.