Highlights Forecasts for the future patterns of COVID-19 in top five affected countries. Causal impacts of lockdowns in the top five affected countries. Improved forecasts under Bayesian Structural Time Series Models. Investigation of trend, seasonality and regression components separately.

In this paper, the Bayesian estimation of the parameters of mixture of two components of Gumbel type II distribution has been considered. A heterogeneous population has been modeled by means of two components mixture of the Gumbel type II distribution under type I censored data. The Bayes estimators of the said parameters have been derived under the assumption of informative priors using different loss functions. A censored mixture data is simulated by probabilistic mixing for the computational purpose. The comparisons among the estimators have been made in terms of corresponding risks.

Abstract

Mixtures models have received sizeable attention from analysts in the recent years. Some work on Bayesian estimation of the parameters of mixture models have appeared. However, the were restricted to the Bayes point estimation The methodology for the Bayesian interval estimation of the parameters for said models is still to be explored. This paper proposes the posterior interval estimation (along with point estimation) for the parameters of a two-component mixture of the Gompertz distribution. The posterior predictive intervals are also derived and evaluated. Different informative and noninformative priors are assumed under a couple of loss functions for the posterior analysis. A simulation study was carried out in order to make comparisons among different point and interval estimators. The applicability of the results is illustrated via a real life example.

Based on left type II censored samples from a Gumbel type II distribution, the Bayes estimators and corresponding risks of the unknown parameter were obtained under different asymmetric loss functions, assuming different informative and non-informative priors. Elicitation of hyper-parameters through prior predictive approach has also been discussed. The expressions for the credible intervals and posterior predictive distributions have been derived. Comparisons of these estimators are made through simulation study using numerical and graphical methods.