ESTIMATION OF THE PMF AND CDF OF SOME STANDARD DISCRETE DISTRIBUTIONS USEFUL IN RELIABILITY MODELLING

摘要

This article addresses different methods of estimation of the probability mass function (PMF) and cumulative distribution function (CDF) of some standard discrete distributions, viz. Binomial, Poisson and Geometric. Following estimation methods are considered: uniformly minimum variance unbiased estimator (UMVUE), maximum likelihood estimator (MLE), percentile estimator (PCE), least squares estimator (LSE), weighted least squares estimator (WLSE), Bayes estimate (BE). Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation. Finally, real data sets have been analyzed for illustrative purposes.