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Article
Bayesian Estimation for Two Parameters of Gamma Distribution Under Precautionary Loss Function

Journal: Ibn Al-Haitham Journal For Pure And Applied Science مجلة ابن الهيثم للعلوم الصرفة والتطبيقية ISSN: 16094042/ 25213407 Year: 2019 Volume: 32 Issue: 1 Pages: 187-196
Publisher: Baghdad University جامعة بغداد

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Abstract

In the current study, the researchers have been obtained Bayes estimators for the shape andscale parameters of Gamma distribution under the precautionary loss function, assuming thepriors, represented by Gamma and Exponential priors for the shape and scale parametersrespectively. Moment, Maximum likelihood estimators and Lindley’s approximation have beenused effectively in Bayesian estimation.Based on Monte Carlo simulation method, those estimators are compared depending on themean squared errors (MSE’s). The results show that, the performance of Bayes estimator underprecautionary loss function with Gamma and Exponential priors is better than other estimates inall cases.


Article
Bayesian Inference for the Parameter and Reliability Function of Basic Gompertz Distribution under Precautionary loss Function

Authors: Manahel Kh. Awad --- Huda A. Rasheed
Journal: Ibn Al-Haitham Journal For Pure And Applied Science مجلة ابن الهيثم للعلوم الصرفة والتطبيقية ISSN: 16094042/ 25213407 Year: 2020 Volume: 33 Issue: 2 Pages: 140-148
Publisher: Baghdad University جامعة بغداد

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Abstract

In this paper, some estimators for the unknown shape parameter and reliability function ofBasic Gompertz distribution have been obtained, such as Maximum likelihood estimator andBayesian estimators under Precautionary loss function using Gamma prior and Jefferys prior.Monte-Carlo simulation is conducted to compare mean squared errors (MSE) for all theseestimators for the shape parameter and integrated mean squared error (IMSE's) for comparingthe performance of the Reliability estimators. Finally, the discussion is provided to illustratethe results that summarized in tables.

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