Generalized Inverted Exponential Distribution: Different Methods of Estimation

SYNOPTIC ABSTRACT

In this article we consider various methods of estimation of the unknown parameters of a generalized inverted exponential distribution from a frequentist as well as Bayesian perspective. With regard to Bayes estimation of the unknown parameters under squared error loss function, we assume that the scale and shape parameters of the distribution have a gamma prior and are independently distributed. Under these priors, we use an importance sampling technique to calculate Bayes estimates and the corresponding highest posterior density intervals. We also compute approximate Bayes estimates using Lindley’s approximation. Besides Bayes estimation, we introduce maximum likelihood estimates and estimates based on percentiles. Monte Carlo simulations are performed to compare the performance of the Bayes estimates with the classical estimates. Two datasets have been analyzed for illustrative purposes.

Key Words and Phrases::

• Bayes estimator
• maximum likelihood estimator
• percentile estimator
• importance sampling
• Lindley’s approximation
• highest posterior density interval.