On the infinite divisbility of the Pareto distribution

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Abstract
That the Pareto distribution is infinitely divisible is a simple consequence of an important theorem by Goldie and Steutel if an observation by Thyrion is used. In the present paper the author investigates the Pareto distribution more closely and proves that it belongs to a well-known subclass of the class of infinitely divisible distributions, the so called class L. That is achieved by showing that the Pareto distribution can be viewed as a “generalized Γ-convolution”. The corresponding problem concerning the lognormal distribution is briefly touched upon.

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