Different methods of estimation in two parameter Geometric distribution with randomly censored data

Random censoring scheme has been extensively discussed in literature for several statistical distribution models. Most of these studies focus on continuous variables with range 0 to infinity. In this paper the lifetime and censoring time variables are assumed to be discrete and a minimum threshold is assumed as a location parameter for failure and censoring times. Here, we study a two parameter geometric distribution with location parameter mu and probability parameter theta using randomly censored data. The importance of the minimum time location parameter is highlighted over the no location parameter case with an example. Some classical estimation methods such as methods of moments, least squares, L-moments and maximum likelihood estimation (MLE) are discussed. Asymptotic confidence intervals for parameters are derived using MLEs. Expected time on test is obtained for the parameters. Bayes estimators are developed under generalized entropy loss function (GELF) assuming informative as well as non-informative priors of the parameters. Maximum likelihood and Bayes estimates under GELF are also developed for the reliability characteristics. Various estimation procedures are compared using a Monte Carlo simulation study. The effect and importance of the minimum threshold parameter is illustrated with a numerical data example.