Statistical Inference for the Inverse Lindley Distribution Based on Lower Record Values

Accepted - January 2024

Abstract

In this paper, we discuss the problem of classical and Bayesian estimation of the parameter of the inverse Lindley distribution based on lower records as well as the prediction of its future record values. We obtain the (ML) estimator, the approximate confidence interval, and two boot-strap types for the parameter based on $ILD$ records. In the context of Bayesian estimation, we use Tierney Kadane and MCMC methods. The future record values were also explored using the ML and Bayesian approaches. The highest conditional density as well as credible intervals are also constructed for a future lower record.