Approximate Estimation Methods for Exponential Rayleigh Distribution

Shurooq A.K. AL-Sultany; Lamyaa Khalid  Hussein

doi:10.24996/ijs.2025.66.8.21

Authors

Shurooq A.K. AL-Sultany Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq https://orcid.org/0000-0002-3423-875X
Lamyaa Khalid Hussein Department of Mathematics and Computer Applications, College of Sciences, Al-Nahrain University, Jadriya, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2025.66.8.21

Keywords:

Exponential Rayleigh Distribution, Modified Maximum Likelihood, Bayes Estimation, Lindley’s Approximation, scale invariant squared Error Loss Function, Squared Error Loss Function, linear-exponential (Linex) Loss Function, precautionary Loss Function

Abstract

This paper introduces approximate estimators for the scale parameters, reliability, and hazard rate functions of the exponential Rayleigh distribution using Modified Maximum Likelihood and Bayesian method. The Modified Maximum Likelihood estimator requires iterative techniques such as the modified Newton–Raphson method due to the unavailability of closed-form expressions. Bayesian estimators are derived using both symmetric and asymmetric loss functions, and Lindley's approximation method is employed for integrals that lack closed-form solutions. Finally, the estimators obtained are compared through Monte Carlo simulation study.