Estimation of the PDF and the CDF of exponentiated moment exponential distribution

Abstract

This article addresses the different methods of estimation of the probability density function and the cumulative distribution function for the exponentiated moment exponential distribution. Following estimation methods are considered: uniformly minimum variance unbiased estimators, maximum likelihood estimators, percentile estimators, least squares estimators, weighted least square estimators, maximum product of spacings estimators, Cramer–von-Mises estimators and Anderson–Darling estimators. Analytical expressions are derived for the bias and the mean squared error. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. Simulation studies and real data applications show that the ML estimator performs better than others. Finally, one real data set has been analyzed for illustrative purposes.