Bayesian inference on the shape parameter and future observation of exponentiated family of distributions (Q764411)

Summary: Bayes estimators of the shape parameter of exponentiated family of distributions have been derived by considering extensions of Jeffreys' noninformative as well as conjugate priors under different scale-invariant loss functions, namely, the weighted quadratic loss function, squared-log error loss function and general entropy loss function. The risk functions of these estimators have been studied. We have also considered the highest posterior density (HPD) intervals for the parameter and the equal-tail and HPD prediction intervals for future observation. Finally, we analyze a data set for illustration.