Lindley’s approximation in estimating two-parameters inverted weighted exponential distribution - Nazri, Fatin Syazwani; Zulkafli, Hani Syahida (Penerbit UMT, 2025)
The Inverted Weighted Exponential (IWE) distribution can be used to describe and model real-life phenomena with unimodal or decreasing failure rates. The main aim of this study is to use the Bayesian approach to estimate the two parameters of the distribution. Two loss functions are used, the Squared Error Loss Function (SELF) and Linear Exponential (LINEX) loss function, using Lindley’s method. The Root Mean Square Error (RMSE) is reviewed to assess the performance of the estimation method. The results of simulation studies reveal that the scale parameter benefitted from using the Bayesian approach with a SELF. This paper mainly aims to demonstrate how the Bayesian framework can be used to estimate the parameters of the IWE distribution in addition to the conventional Maximum Likelihood estimation (MLE). A detailed simulation study is conducted to compare the performance of the Bayesian estimator and the non-Bayesian estimator, i.e., MLE. The Bayesian approach uses Lindley’s approximation with SELF and LINEX functions. The empirical results demonstrate that the scale parameter of the IWE distribution benefitted from using the Bayesian approach with a SELF. The estimators also perform better with a larger sample size, n. Nevertheless, no similar work has used Bayesian estimation for the parameters of the IWE distribution.