Weighted Cramer-von Mises estimation of a distribution

Dustin Dean Ruff, Purdue University

Abstract

The scope of this present work is to develop an estimation procedure which fits a probability distribution to data when it is most important that the fitted distribution model the lower possible values (the lower tail) tightly. We also want the resulting procedure to be relatively easy to use and be easy to adapt to any assumed parametric family. Our approach to this task is to consider the class of minimum distance Cramer-von Mises estimation procedures and pick out subclasses of these procedures which correspond to three different weightings. Formulas to aid in the calculation of these estimators are derived and the changes in estimates within each class of weights are investigated. The use of our method to determine collections of models which would fit are also discussed. These estimation methods are then compared with other, standard methods in cases where tail sensitivity may be needed. In addition, we find formulas for calculating any minimum-distance estimator which is tail sensitive and give methods for using these estimators, as with the other estimators, to find a collection of models which would fit reasonably well. Finally, a case study using airplane fatigue data is given. Our estimation method is found to satisfy our concerns and compete quite competently with other methods under good conditions. When the fitted family only has a distribution which fits the tail values of the data, our method consistently outperforms the standard methods. Thus we have developed a useful, easy to use estimation procedure which satisfies our concerns.

Degree

Ph.D.

Advisors

McCabe, Purdue University.

Subject Area

Statistics

COinS