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

TL;DR

This paper develops classical and Bayesian methods for estimating parameters of the Gumbel type-II distribution from censored data, applying these techniques to Covid-19 death rate data in India.

Contribution

It introduces Bayesian estimation techniques using MCMC for Gumbel type-II parameters under AT-II PHCS, with comprehensive interval estimation and real data application.

Findings

Bayesian estimates obtained via MCMC are effective.

Interval estimates include bootstrap and HPD credible intervals.

Application to Covid-19 data demonstrates practical utility.

Abstract

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.