A comparison of estimation techniques for the three parameter pareto distribution

Abstract

This paper compares minimum distance estimation with best linear unbiased estimation to determine which technique provides the most accurate estimates for location and scale parameters as applied to the three parameter Pareto distribution. Two minimum distance estimators are developed for each of the three distance measures used (Kolmogorov, Cramer‐von Mises, and Anderson‐Darling) resulting in six new estimators. For a given sample size 6 or 18 and shape parameter 1(1)4, the location and scale parameters are estimated. A Monte Carlo technique is used to generate the sample sets. The best linear unbiased estimator and the six minimum distance estimators provide parameter estimates based on each sample set. These estimates are compared using mean square error as the evaluation tool. Results show that the best linear unbaised estimator provided more accurate estimates of location and scale than did the minimum estimators tested.

Keywords:

• empirical distribution function
• statistical analysis
• Pareto distribution
• Monte Carlo method
• order statistics
• best linear unbaiased estimator
• minimum distance estimator
• Kolmogorov distance
• Anderson‐Darling distance
• Cramer‐von Mises distance