Estimating parameters from the generalized inverse Lindley distribution under hybrid censoring scheme

Estimation of parameters of the generalized inverse Lindley (GIL) distribution is considered under a hybrid censoring scheme. The point estimators, such as the maximum likelihood estimators using the Expectation-Maximization (E-M) algorithm, have been derived. The two approximate Bayes estimators using Tierney and Kadane's method and Gibbs sampling procedure, using the gamma prior and the general entropy loss (GEL) function, have been obtained. Several confidence intervals are proposed, such as the asymptotic confidence intervals (ACIs), bootstrap confidence intervals, and the highest posterior density (HPD) credible intervals. The prediction for future observations has been considered under one and two-sample Bayesian prediction methods using the type-i hybrid censoring scheme. An extensive simulation study has been conducted to numerically evaluate all the estimators' performances. The point estimators are compared through their biases and mean squared errors (MSEs). The performances of confidence intervals are evaluated using coverage probability (CP), average length (AL), and probability coverage density (PCD). Two real-life datasets have been considered for illustrative purposes.

Automated summary

This study considers the estimation of parameters for the generalized inverse Lindley (GIL) distribution and proposes point estimators and Bayesian estimators. It also introduces various confidence interval methods and prediction methods, which are evaluated and validated through simulation studies and real-life datasets.