Parameter estimation for reduced Type-I Heavy-Tailed Weibull distribution under progressive Type-II censoring scheme

Reduced Type-I heavy-tailed Weibull (RTI-HTW) distribution is a particular case of the Type-I heavy-tailed family of distributions. This article has studied the properties, inference and real-life applications of RTI-HTW distribution. Firstly, properties such as quantile function, moment-generating function, stress–strength reliability, measure of uncertainty, and mean residual life have been discussed. Further, the inference of RTI-HTW distribution has been discussed under classical and Bayesian frameworks. We have studied the point and interval estimations of model parameters under the progressive Type-II censoring scheme. Four point estimation methods have been used to find the point estimates, such as maximum likelihood estimate (MLE), improved MLE, and Bayesian estimates under informative and kernel priors. Additionally, the approximate confidence interval has been calculated using MLEs, whereas the credible interval has been derived using the Bayesian estimates under informative prior. A Monte Carlo simulation study has been discussed to compare the results of all methods. To illustrate the practical applicability of the proposed model and methodologies, we have analyzed two real-world data sets: the mortality rate of COVID-19 patients in Canada and the infant mortality rate in China. Numerical results demonstrate that the proposed model provides a good fit for both data sets, and the estimation methods discussed are effective and satisfactory.