Studies on properties and estimation problems for modified extension of exponential distribution

TL;DR

This paper introduces a modified exponential distribution with three parameters, explores its properties, and develops Bayesian estimation methods including Gibbs sampling, comparing them with classical estimators through simulations and real data analysis.

Contribution

It proposes a new three-parameter modified exponential distribution and develops Bayesian estimation techniques using Lindley's approximation and Gibbs sampling.

Findings

Bayesian estimators outperform classical ones in simulated risk.

Gibbs sampling effectively estimates parameters and credible intervals.

The distribution's properties are suitable for reliability analysis.

Abstract

The present paper considers modified extension of the exponential distribution with three parameters. We study the main properties of this new distribution, with special emphasis on its median, mode and moments function and some characteristics related to reliability studies. For Modified- extension exponential distribution (MEXED) we have obtained the Bayes Estimators of scale and shape parameters using Lindley's approximation (L-approximation) under squared error loss function. But, through this approximation technique it is not possible to compute the interval estimates of the parameters. Therefore, we also propose Gibbs sampling method to generate sample from the posterior distribution. On the basis of generated posterior sample we computed the Bayes estimates of the unknown parameters and constructed 95 % highest posterior density credible intervals. A Monte Carlo simulation study is carried out to compare the performance of Bayes estimators with the corresponding classical estimators in terms of their simulated risk. A real data set has been considered for illustrative purpose of the study.