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