Statistical Inference of Exponentiated Moment Exponential Distribution Based on Lower Record Values

Abstract

Based on lower record values, we first derive the exact explicit expressions as well as recurrence relations for the single and product moments of record values and then use these results to compute the means, variances and coefficient of skewness and kurtosis of exponentiated moment exponential distribution (EMED), a new extension of moment exponential distribution, recently introduced by Hasnain (Exponentiated moment exponential distribution. Ph.D. Thesis, 2013). 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 also derived the Bayes interval of this distribution and discussed both frequentist and the Bayesian prediction intervals of the future record values based on the observed record values. Monte Carlo simulations are performed to compare the performances of the proposed methods, and a data set has been analyzed for illustrative purposes.

Keywords

Lower record values / Single and product moments / Recurrence relations / Bayes estimator / General entropy loss function / Maximum likelihood estimator