Bayesian Framework of Exponentiated Odd Lomax Exponential Distribution: Application to Student Satisfaction and Academic Achievement Data

Abstract

Bayesian inference updates prior beliefs with new evidence providing a mathematically rigorous, quantified measure of uncertainty. The aim of this study is to derive the Bayesian framework for the EOLE distribution using a Gamma prior. It subsequently derives a Bayesian regression model for the EOLE distribution by utilizing Gamma and Normal distributions as priors.  The proposed model was empirically validated through a dataset of student satisfaction and academic achievement. Data from 628 respondents were collected via random sampling across 32 campuses at eight universities, utilizing a survey technique. Parameters of the proposed distribution were estimated using the MLE technique under the classical framework and the MCMC technique under the Bayesian framework, along with its regression model. For Bayesian inference, diagnostic tests of MCMC chains included trace plots, ergodic mean plots, autocorrelation, and prior and posterior predictive checks under graphical assessment, as well as effective sample size and $\hat{R}$  under numerical assessment. The estimated parameters from the Bayesian model and its regression model were consistent with the MLE technique. Hence, the Bayesian model of EOLE distribution is an alternative model for the analysis of educational data.