Statistical Inference to the Parameter of the Inverse Power Ishita Distribution under Progressive Type-II Censored Data with Application to COVID-19 Data

Abstract

The goal of the article is the inference about the parameters of the inverse power ishita distribution (IPID) using progressively type-II censored (Prog–II–C) samples. For IPID parameters, maximum likelihood and Bayesian estimates were obtained. Two bootstrap “confidence intervals” (CIs) are also proposed in addition to “approximate confidence intervals” (ACIs). In addition, Bayesian estimates for “squared error loss” (SEL) and LINEX loss functions are provided. The Gibbs within Metropolis–Hasting samplers process is used to provide Bayes estimators of unknown parameters also “credible intervals” (CRIs) of them by using the “Markov Chain Monte Carlo” (MCMC) technique. Then, an application of the suggested approaches is considered a set of real-life data this data set COVID-19 data from France of 51 days recorded from 1 January to 20 February 2021 formed of mortality rate. To evaluate the quality of the proposed estimators, a simulation study is conducted.