Minimum Distance Estimation of the Three Parameters of the Gamma Distribution

Abstract

Procedures have been investigated to establish robust, adaptive estimating techniques for the 3-parameter Gamma distribution, The procedures incorporate minimum distance statistics for determining the location parameter for a range of sample sizes and shape parameters. Seven new estimators were developed of which six incorporate minimum distance estimation for determining the location parameter or guaranteed life with the remaining parameters estimated by maximum likelihood. All the estimators were compared with maximum likelihood estimators (MLEs) using 1000 Monte Carlo repetitions. The criteria of comparison was the ratio of the mean square errors of the parameter estimates. All the new estimators give better results than the MLE. The minimum distance estimation of the location parameter using the Anderson Darling goodness of fit statistic provided the overall best estimates of the parameters. As the sample size increased the relative position of MLEs improved but were still very inefficient with respect to best of the new estimators at sample size 20.