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In this paper, we investigate the classical and Bayesian estimation ofunknown parameters of the Gumbel type-II distribution based on adaptive type-IIprogressive hybrid censored sample (AT-II PHCS). The maximum likelihoodestimates (MLEs) and maximum product spacing estimates (MPSEs) are developedand computed numerically using Newton-Raphson method. Bayesian approaches areemployed to estimate parameters under symmetric and asymmetric loss functions.Bayesian estimates are not in explicit forms. Thus, Bayesian estimates areobtained by using Markov chain Monte Carlo (MCMC) method along with theMetropolis-Hastings (MH) algorithm. Based on the normality property of MLEs theasymptotic confidence intervals are constructed. Also, bootstrap intervals andhighest posterior density (HPD) credible intervals are constructed. Further aMonte Carlo simulation study is carried out. Finally, the data set based on thedeath rate due to Covid-19 in India is analyzed for illustration of thepurpose.

Estimation of parameters of the Gumbel type-II distribution under AT-II PHCS with an application of Covid-19 data