Comparison of Estimation Techniques for the Four Parameter Beta Distribution.

This thesis compares three estimation techniques in application to the beta distribution method of moments, maximum likelihood, and minimum distance. The four parameter version of the beta distribution is used it has two shape parameters, and upper and lower limit parameters. Linear interpolation on order statistics is used to find initial estimates of the limits. The classical estimation procedures, method of moments and maximum likelihood, are applied through procedures found in the literature. A newer technique, minimum distance, is applied for the first time to the beta distribution. Comparison of estimation techniques is accomplished using Monte Carlo analysis. Five sample sizes are considered -- 4, 8, 12, 16, and 20 -- and three pairs of shape parameters -- 3,3, 9,4, and 1,2 -- for a total of fifteen cases. One thousand samples are generated for each case, and each estimation technique is then applied to all samples.