Estimation of Parameters for Inverse Power Ailamujia and Truncated Inverse Power Ailamujia Distributions Based on Progressive Type-II Censoring Scheme

Accurate estimation and modeling of infant mortality rates are crucial for public health planning, medical research, and policy-making. Many biological, environmental, and socio-economic factors influence infant mortality. It is essential to employ robust statistical models that can detect the underlying failure patterns. Traditional lifetime models are incapable of capturing infant mortality patterns due to their complexity, particularly when decreasing failure rates occur over time. We introduce the Inverse Power Ailamujia (IPA) and Truncated Inverse Power Ailamujia (TIPA) distributions as a generalizable lifetime model specifically designed to represent decreasing failure rates, making it highly suitable for analyzing infant mortality data. For the mortality studies, it is often not possible to complete data gathering due to the limitations in cost and time, and hence one resorts to a progressive censoring scheme where only a subset of the observed failures is recorded while the remaining units are progressively censored. Progressive censoring with the IPA and TIPA framework is employed to facilitate data collection. The maximum likelihood estimation (MLE) and Bayesian inference are employed to estimate the IPA and TIPA model's unknown parameters under progressive censoring. The Bayesian approach is explored under symmetric squared error and asymmetric LINEX loss functions, providing robust estimation techniques that account for different levels of parameter uncertainty. Additionally, confidence intervals and credible intervals are constructed using bootstrap methods, asymptotic approximations, and Markov Chain Monte Carlo (MCMC) simulations, ensuring the reliability of parameter estimates. The effectiveness of the proposed approach is demonstrated through a two real-world dataset, where the IPA and TIPA models predicts. The findings highlight the advantages of integrating progressive censoring with the IPA and TIPA distributions, offering a practical and computationally efficient tool for modeling.