Robust Minimum Distance Estimation of the Four-Parameter Generalized Gamma Distribution

摘要

A robust estimation technique (MLDE) is developed which uses minimum distance estimation in conjunction with maximum likelihood estimation (MLE). This technique is then applied to the four-parameter generalized Gamma distribution to obtain location, scale, shape, and power parameter estimates. A Monte Carlo analysis is conducted on three members of the four-parameter generalized Gamma distribution with sample sizes of 12, 16, 20, and 24 for a total of twelve cases. For each of these twelve cases, one thousand samples are generated for the analysis. Initial estimates of the location, scale, shape, and power parameters are found using a maximum liklihood estimator. Minimum distance estimation using the Anderson-Darling statistic is then employed to obtain a new estimate of the location parameter. Finally, this new improved location parameter estimate is used to refine the scale, shape, and power parameter estimates through maximum likelihood estimation. The performance of the MLDE technique is determined through use of mean square error and relative efficiency measures. (Author)