A Suitable Alternative to the Pareto Distribution

Year 2014, Volume: 43 Issue: 5, 843 - 860, 01.10.2014

Emilio Gómez–déniz Enrique Calderín–ojeda

Abstract

Undoubtedly, the single parameter Pareto distribution is one of the
most attractive distribution in statistics; a power law probability distribution found in a large number of real-world situations inside and
outside the field of economics. Furthermore, it is usually used as a basis
for excess of loss quotations as it gives a pretty good description of the
random behaviour of large losses. In this paper, we introduce a distribution which can be considered as alternative to the single parameter
Pareto distribution. A comprehensive treatment of its mathematical
properties is considered with relevant emphasis on results concerning
insurance. Additionally, estimation by the method of moments and
maximum likelihood is discussed. Then, an analysis of estimation performance is carried out. Finally, the performance of the model is examined by using two examples of real claims data.

Keywords

Credibility , excess-of-loss reinsurance , Pareto Distribution , Gamma Distribution , Ruin Function , Threshold

References

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