Asymmetric Randomly Censored Mortality Distribution: Bayesian Framework and Parametric Bootstrap with Application to COVID‐19 Data

Abstract

This article investigates a survival analysis under randomly censored mortality distribution. From the perspective of frequentist, we derive the point estimations through the method of maximum likelihood estimation. Furthermore, approximate confidence intervals for the parameters are constructed based on the asymptotic distribution of the maximum likelihood estimators. Besides, two parametric bootstraps are implemented to construct the approximate confidence intervals for the unknown parameters. In Bayesian framework, the Bayes estimates of the unknown parameters are evaluated by applying the Markov chain Monte Carlo technique, and highest posterior density credible intervals are also carried out. In addition, the Bayes inference based on symmetric and asymmetric loss functions is obtained. Finally, Monte Carlo simulation is performed to observe the behavior of the proposed methods, and a real data set of COVID-19 mortality rate is analyzed for illustration.

Bayesian Inferential Approaches and Bootstrap for the Reliability and Hazard Rate Functions under Progressive First-Failure Censoring for Coronavirus Data from Asymmetric Model

“…where ζ = α, β, δ, λ, r(t) or h(t). For more accurate and important details, see EL-Sagheer et al [25]. It is clear that the integrals in ( 15) and ( 16) cannot be computed in closed forms.…”

Bayesian Prediction Intervals Based on Type‐I Hybrid Censored Data from the Lomax Distribution under Step‐Stress Model

“…Also, in many practical situations, although the dependent prior models seem more attractive, yet the dependent property between parameters cannot be justifed from a statistical perspective due to historical information and expert experience where such prior data/information may be very rare. Terefore, independent priors are more popular in statistics under the Bayesian procedure for the sake of simplicity, see EL-Sagheer et al [31]; and Nassar et al [32].…”

On basic life testing issues in medical research using non‐parametric hypothesis testing

“…Increasing failure rate (IFR), New better than used (NBU), Used better than age (UBA), and EBU are the most popular of these classes, Navarro and Pellerey, 1 Barlow and Proschan, 2 Bryson and Siddiqui, 3 Navarro, 4 and Esary et al 5 Other aging categories, such as Laplace ordering, and the order of moment generating function for these categories have been considered by many researchers. Fernandez-Ponce et al, 6 Ahmad, 7 Abu Youssef et al, 8 Etman et al, 9 EL-Sagheer et al, 10 Abu-Youssef et al, 11 Bakr et al, 12 EL-Sagheer et al, 13 Mahmoud et al 14 and Gadallah et al 15 The fundamental needs of contemporary science and technology compelled the development of a systematic approach for the investigation of any event or activity taking place in the world. As a result, it makes sense that such an approach would be required in the investigation of the reliability of technological systems and products.…”

“…Other aging categories, such as Laplace ordering, and the order of moment generating function for these categories have been considered by many researchers. Fernandez‐Ponce et al., 6 Ahmad, 7 Abu Youssef et al., 8 Etman et al., 9 EL‐Sagheer et al., 10 Abu‐Youssef et al., 11 Bakr et al., 12 EL‐Sagheer et al., 13 Mahmoud et al 14 . and Gadallah et al 15 …”