Bayesian Estimation of Shape Parameter of Generalized Inverse Exponential Distribution Under the Non-Informative Priors

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– Bayesian Estimation of Shape Parameter of Generalized Inverse Exponential Distribution Under the Non-Informative Priors –

Download Bayesian Estimation of Shape Parameter of Generalized Inverse Exponential Distribution Under the Non-Informative Priors. Statistics students who are writing their projects can get this material to aid their research work.

Abstract

In this research, the shape parameter of the Generalized Inverse Exponential Distribution (GIED) was estimated using maximum likelihood and Bayesian estimation techniques.

The Bayes estimates were obtained under the squared error loss function and precautionary loss function under the assumption of two non-informative priors.

An extensive Monte Carlo simulation study was carried out to compare the performances of the Bayes estimates with that of the maximum likelihood estimates at different sample sizes.

The Extended Jeffrey’s prior was observed to have estimated the shape parameter of the GIED better when compared with the maximum likelihood estimator and other Bayes estimate at all sample sizes using their mean squared error.

Introduction

In the past, many generalized univariate continuous distribution have been proposed. The generalization of these distributions is important in order to make its shape more flexible to capture the diversity present in the observed dataset.

One of such generalizations is the Generalized Inverse exponential distribution (GIED) proposed by Abouammoh and Alshangiti (2009),

in which the shape parameter was added to make the distribution more flexible. As a result, this parameter has to be estimated using the appropriate estimation technique.

One of such techniques is the Bayesian method of estimation which combines the prior knowledge with new observations to come up with updated information.

Researchers have estimated the parameter of different distributions using the Bayesian technique because of its advantage over other methods of estimation.

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