Moments and Estimation of the Exponentiated Moment Exponential Distribution

Abstract

A new extension of moment exponential distribution, called exponentiated moment exponential distribution (EMED), was recently introduced by Hasnain [14]. Based on lower generalized order statistics, we first derive the explicit expressions as well as recurrence relations for single and product moments of lower generalized order statistics and we use these results to compute the means, variances and coefficients of skewness and kurtosis of EMED. Further, using a recurrence relation for single moment, we obtain characterization of EMED. Next we obtain the maximum likelihood estimators of the unknown parameters and the approximate confidence intervals of the EMED. Finally, we consider Bayes estimation under the symmetric and asymmetric loss functions using gamma priors for both shape and scale parameters. We have are also derived the Bayes interval of this distribution. Monte Carlo simulations are performed to compare the performances of the proposed methods.