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.