Asymptotic Distributions of the Estimated survival functions of the Exponential, Geometric and BEG Distributions

Abstract

In this work, we derive the limiting normal distributions of the maximum likelihood estimators of the survival functions for the exponential, geometric and (bivariate) BEG distributions. We discuss the monotonicity of the variance of the limiting distribution for exponential and geometric cases. Finally, we illustrate the convergence of the empirical distribution of the survival function to the limiting normal law using Monte Carlo simulations.