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In this paper, different estimation is discussed for a general family of inverse exponentiated distributions. Under the classical perspective, maximum likelihood and uniformly minimum variance unbiased are proposed for the model parameters. Based on informative and non-informative priors, various Bayes estimators of the shape parameter and reliability function are derived under different losses, including general entropy, squared-log error, and weighted squared-error loss functions as well as another new loss function. The behavior of the proposed estimators is evaluated through extensive simulation studies. Finally, two real-life datasets are analyzed from an illustration perspective.