Bayesian and non-Bayesian inferential approaches under lower-recorded data with application to model COVID-19 data

In this article, estimation of the parameters as well as some lifetime parameters such as reliability and hazard rate functions for the Dagum distribution based on record statistics is obtained. Both Bayesian and non-Bayesian inferential approaches of the distribution parameters and reliability characteristics are discussed. Moreover, approximate confidence intervals for the parameters based on the asymptotic distribution of the maximum likelihood estimators are constructed. Besides, to construct the variances of the reliability and hazard rate functions the delta method is implemented. The Lindley's approximation and Markov chain Monte Carlo techniques are proposed to construct the Bayes estimates. To this end, the results of the Bayes estimates are obtained under both symmetric and asymmetric loss functions. Also, the corresponding highest posterior density credible intervals are constructed. A simulation study is utilized to assay and evaluate the performance of the proposed inferential approaches. Finally, a real data set of COVID-19 mortality rate is analyzed to illustrate the proposed methods of estimation.