Abstract
Pareto variables are widely used. It is useful to be able to obtain the distribution of some simple functions of Pareto variables in a convenient manner. The Mellin transform with its convolution and exponentiation properties is utilized to that end. Specifically, expressions are written for products, quotients, and sums of products of Pareto variables. These include the distribution of the geometric mean and the product of minimum values of Pareto variables.
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The Office of Naval Research partially supported the work under Contract No. N000-14-75-C-0254.
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Lorah, D.J., Stark, R.M. On elementary functions of Pareto variables. Metrika 25, 59–63 (1978). https://doi.org/10.1007/BF02204351
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DOI: https://doi.org/10.1007/BF02204351