  In this article we show the relationship between the Pareto distribution and
the gamma distribution. This shows that the second one, appropriately extended,
explains some anomalies that arise in the practical use of extreme value
theory. The results are useful to certain phenomena that are fitted by the
Pareto distribution but, at the same time, they present a deviation from this
law for very large values. Two examples of data analysis with the new model are
provided. The first one is on the influence of climate variability on the
occurrence of tropical cyclones. The second one on the analysis of aggregate
loss distributions associated to operational risk management.
