Eslam Abdelhakim Seyam
Department of Insurance and Risk Management, College of Business, Imam Mohammad Ibn Saud Islamic University (IMSIU)
E. M. Moustafa
Department of Statistics and Insurance, Faculty of Commerce, Zagazig University, Zagazig
Although the generalized exponential (GE) distribution is a versatile distribution for modeling lifetime data, there has been no study on the estimation of the distribution parameters using the adaptive Type-II progressive hybrid censoring (AT-II PHC) scheme. This study extends the maximum likelihood estimation (MLE) approach by applying the Newton-Raphson optimization method on the log-transformed parameter space, the Bayesian approach by employing the random walk Metropolis-Hastings (MH) algorithm in combination with Robbins-Monro adaptation and log-normal proposals, and the parametric bootstrap approach for the estimation of the GE distribution parameters. Two priors are employed in the study: a non-informative Gamma(0.001, 0.001) prior and a data-adaptive weakly informative Gamma(1, 1/MLE) prior. Using a Monte Carlo simulation study with M = 200 runs across six plans, it is observed that the RMSE of the estimator of α decreases from 2.3079 (n = 20) to 0.7145 (n = 50), a reduction of 69%. Furthermore, Prior 2 outperforms the other priors in each case by providing the smallest RMSE for all the parameters. The HPD interval coverage probabilities vary from 0.8950 to 0.9650 for different plans, which is greater than the ACI-NL approach, which provides a coverage probability between 0.7100–0.8900. Two real-life datasets are analyzed in the study. The first dataset is the remission times of patients suffering from acute myelogenous leukemia (AML), and the second dataset is the failure times of Kevlar 49/epoxy strands. Using the AT-II PHC scheme for the first dataset (n = 23, m = 17), it is observed that the MLE and Bayesian posterior means for the GE distribution parameters differ by only 2.03%. The Kolmogorov-Smirnov test for goodness-of-fit is performed for the data, which indicates a satisfactory fit for the GE distribution (p = 0.6714). Using the AT-II PHC scheme for the second dataset (n = 49, m = 35), it is observed that the GE distribution is inadequate for modeling the data (p = 0.0137), and the MCMC process does not converge (ESS < 173 and |Geweke Z| > 1.96), indicating model inadequacy. Model selection is performed using AIC, BIC, and DIC criteria.
