Bayes Estimators for the Parameter of the Inverted Exponential Distribution under Symmetric and Asymmetric Loss Functions

Abstract

This paper is devoted to discuss Bayes method to estimate the unknown scale parameter of the inverted exponential distribution along with the maximum likelihood method. Bayes estimators are obtained under symmetric "squared error" and asymmetric "precautionary" loss functions corresponding to informative "inverted gamma and Gumbel type II" and non-informative "Jeffrey and extension of Jeffrey" priors. The obtained Bayes estimators along with the maximum likelihood estimator are compared empirically for different cases and sample sizes using Monte-Carlo simulation method in terms of two statistical criteria which are mean squared error (MSE) and mean absolute percentage error (MAPE). Among the set of conclusions that have been reached, it is observed that, conjugate inverted gamma prior with hyper-parameters  and  record full appearance as best prior depending on the value of the parameter of inverted exponential distribution.

Keywords: Inverted exponential distribution; maximum likelihood estimator; Bayes estimator; informative prior; non-informative prior; squared error loss function; precautionary loss function; mean squared error; mean absolute percentage error.