Document Type : Original Article

Authors

• Mehrdad Norouzi Firooz ¹
• Hossein Jabbari Khamnei ¹
• Ali Akbar Heydari ²

¹ Department of Statistics, Faculty of Mathematics, Statistics, and Computer Science, University of Tabriz, Tabriz, Iran

² 29 Bahman Boulevard, Tabriz

Abstract

This paper presents a comprehensive study on statistical inference for the Lindley-Exponential (LE) distribution based on lower record values. We derive key distributional properties of the LE model, including the density and moments of lower record statistics. Both classical and Bayesian frameworks are developed for parameter estimation. The maximum likelihood method is employed to obtain point estimates and asymptotic confidence intervals. For the Bayesian approach, independent gamma priors are assumed for the parameters, and estimation is conducted under symmetric (squared error) and asymmetric (LINEX) loss functions. Due to the analytical intractability of the posterior distributions, the Tierney-Kadane approximation and a Metropolis-Hastings within Gibbs sampling algorithm are utilized for computation. Furthermore, we address the problem of predicting future lower record values using both maximum likelihood and Bayesian predictive distributions. Extensive Monte Carlo simulations are conducted to evaluate the performance of the proposed estimators and predictors. The results indicate that the Bayesian estimators under squared error loss often yield lower expected risks, and the predictive accuracy improves with the number of observed records. The methodologies developed in this study are particularly useful for modeling and predicting extreme or record-breaking events in fields such as reliability engineering, meteorology, and economics.

Keywords

• Lindley-Exponential distribution
• Maximum likelihood estimation
• Lower record values
• Predictive distribution