Bayesian Approximation Techniques for the Generalized Inverted Exponential Distribution Rana A. Bakoban and Maha A. Aldahlan* Department of Statistics, College of Science, University of Jeddah, Jeddah, Saudi Arabia  Corresponding Author: Maha A. Aldahlan. Email: maal-dahlan@uj.edu.sa Received: 22 February 2021; Accepted: 02 May 2021 Abstract: In this article, Bayesian techniques are adopted to estimate the shape parameter of the generalized inverted exponential distribution (GIED) in the case of complete samples. Normal approximation, Lindley’ s approximation, and Tier- ney and Kadane’ s approximation are used for deriving Bayesian estimators. Dif- ferent informative priors are considered, such as Jeffrey’s prior, Quasi prior, modified Jeffrey’s prior, and the extension of Jeffrey’ s prior. Non-informative priors are also used, including Gamma prior, Pareto prior, and inverse Levy prior. The Bayesian estimators are derived under the quadratic loss function. Monte Carlo simulations are carried out to make a comparison among estimators based on the mean square error of the estimates. All estimators using normal, Lindley’ s, and Tierney and Kadane’ s approximation techniques perform consistently since the MSE decreases as the sample size increases. For large samples, estimators based on non-informative priors using normal approximation are usually better than the ones using Lindley’ s approximation. Two real data sets in reliability and medicine are applling to the GIED distribution to assess its flexibility. By comparing the estimation results with other generalized models, we prove that estimating this model using Bayesian approximation techniques gives good results for investigating estimation problems. The models compared in this research are generalized inverse Weibull distribution (GIWD), inverse Weibull distribution (IWD), and inverse exponential distribution (IED). Keywords: Bayesian estimation; generalized inverted exponential distribution; informative and non-informative priors; Lindley’ s approximation; Monte Carlo simulation; normal approximation; Tierney and Kadane’ s approximation 1 Introduction Lifetime models are widely used in the statistical inference field. These models are very important in many areas such as engineering, medicine, zoology, and forecasting. The generalized inverted exponential distribution (GIED) is one of the important lifetime models. It is first proposed by Bakoban et al. [1]. GIED is a flexible model because it has various shapes of the hazard function. This work is licensed under a Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Intelligent Automation & Soft Computing DOI:10.32604/iasc.2022.018041 Article ech T Press Science