Statistical analysis of the Gompertz-Makeham model using adaptive progressively hybrid Type-II censoring and its applications in various sciences

Abstract

Gompertz-Makeham (GomMak) lifetime model has been popularly utilized in explaining human mortality, actuarial tables, growth models, and others. This study focuses on the inference problem of the model parameters and some life parameters, such as the survival (or reliability) and failure rate functions of the GomMak distribution, in the presence of a sample produced from an adaptive progressively hybrid Type-II strategy. To acquire estimates of the unknown objectives, the maximum likelihood and Bayesian estimation approaches are considered. Asymptotic confidence intervals for the same unknown parameters are also estimated based on the observed Fisher information. According to the assumption of gamma intensity introductions, under squared error loss, Bayes’ estimates of various parameters cannot be explicitly expressed. To handle this issue, the Metropolis-Hastings technique is used, in turn, to evaluate the complex Bayes estimates and produce their highest-posterior density interval estimates. Comprehensive numerical examinations, in terms of four-accuracy metrics, namely: root mean squared-error, mean relative absolute-biases, interval lengths, and interval coverage-probabilities, are done to evaluate the supplied estimates. To suggest the best progressive scenario, various optimal criteria are estimated through the offered frequentist estimates. Finally, three applications from the natural sciences—engineering, chemistry, and physics—are utilized to show the utility of the presented methodologies and the possibility of adjusting research aims to real-world problems. Real-world data results stated that the GomMak model provides a useful explanation for various practical situations in the presence of such controlled data.