Numerical Method for Obtaining a Predictive Estimator for the Geometric Distribution

Abstract

An optimal estimator in the light of future data (i.e., a predictive estimator) is obtained using numerical simulations. The predictive estimator is assumed to be one of various functions of the maximum likelihood estimator. We then formulate an estimator that yields better results than the maximum likelihood estimator when the parameters are located within a specific range. Using this method, we derive a predictive estimator for the geometric distribution. This procedure leads to a predictive estimator that outperforms the maximum likelihood estimator in terms of the expected log-likelihood when the parameter is known to be located within a certain range.