Bayesian Estimatiion Of Shape Parameter Of Generalized Inverse Exponential Distribution Under The Non-informative Priors

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. It was found out that the maximum likelihood have the same estimate with the Jeffrey’s prior using the squared error loss function, and also performed better than the Bayes estimates under the Jeffrey’s prior using the precautionary loss function and uniform prior using both loss function but performed lesser than the Extended Jeffrey’s prior under both loss functions. 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. Also the squared error loss function under the Extended Jeffrey’s prior has the best estimate when compared with other Bayes estimates using their posterior risk. Hence the Bayes estimate under the Extended Jeffrey’s using the squared error loss function has the best estimator for estimating the shape parameter of the GIED.

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