Journal of Probability and Statistics
Volume 2009 (2009), Article ID 364901, 10 pages
Research Article

From the General Affine Transform Family to a Pareto Type IV Model

Feldstrasse 145, 8004 Zürich, Switzerland

Received 30 March 2009; Revised 30 September 2009; Accepted 15 October 2009

Academic Editor: José María Sarabia

Copyright © 2009 Werner Hürlimann. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The analytical form of general affine transform families with given maximum likelihood estimators for the affine parameters is determined. In this context, the simultaneous maximum likelihood equations of the affine parameters in the generalised Pareto distribution cannot have a common solution. This pathological situation is removed by extending it to a four parameter family, called Pareto type IV model.