Statistical Inference for the Modified Fréchet–Lomax Exponential Distribution Under Progressive Type‐I Censoring With Applications to Reliability Data

ABSTRACT This paper investigates the Modified Fréchet–Lomax Exponential distribution (MFLE) under the Progressive Type‐I censoring scheme (PrC‐I) for analyzing lifetime data with heterogeneous hazard rate behavior. The PrC‐I scheme is particularly relevant in practical experiments, as it allows progressive removal of surviving units at predetermined times while maintaining a fixed study duration, thus offering greater flexibility and cost efficiency than classical censoring schemes. Parameter estimation is performed using maximum likelihood estimation, parametric bootstrap methods (Bootstrap‐p and Bootstrap‐t), and Bayesian estimation under the squared error loss function. Asymptotic, bootstrap, and Bayesian interval estimates are constructed, and a Markov chain Monte Carlo (MCMC) approach is employed to obtain Bayesian estimates and credible intervals. The performance of the proposed estimators is assessed through Monte Carlo simulations under various sample sizes and censoring scenarios. In addition, the applicability of the MFLE distribution under the PrC‐I scheme is demonstrated using two real COVID‐19 mortality rate datasets from Mexico and Canada. The results indicate that the MFLE model provides an adequate fit and that the PrC‐I framework effectively handles incomplete lifetime data while yielding reliable statistical inferences.