Optimal analysis of adaptive type-II progressive censored for new unit-lindley model

Abstract

The parameters, reliability, and hazard rate functions of the Unit-Lindley distribution based on adaptive Type-II progressive censored sample are estimated using both non-Bayesian and Bayesian inference methods in this study. The Newton–Raphson method is used to obtain the maximum likelihood and maximum product of spacing estimators of unknown values in point estimation. On the basis of observable Fisher information data, estimated confidence ranges for unknown parameters and reliability characteristics are created using the delta approach and the frequentist estimators’ asymptotic normality approximation. To approximate confidence intervals, two bootstrap approaches are utilized. Using an independent gamma density prior, a Bayesian estimator for the squared-error loss is derived. The Metropolis–Hastings algorithm is proposed to approximate the Bayesian estimates and also to create the associated highest posterior density credible intervals. Extensive Monte Carlo simulation tests are carried out to evaluate the performance of the developed approaches. For selecting the optimum progressive censoring scheme, several optimality criteria are offered. A practical case based on COVID-19 data is used to demonstrate the applicability of the presented methodologies in real-life COVID-19 scenarios.

Keywords

• Adaptive Type-II progressive censoring
• Bayesian estimator
• Bootstrapping
• Metropolis-Hasting algorithm
• Reliability
• Unit-Lindley distribution