Abstract
A slight extension of the transform method by Efron (1982) is used to analyze general affine transforms of arbitrary random variables. Our application concerns the simple question “Why is the Pareto an exponential transform?”. This result, already known to Gumbel (1958), finds a satisfactory mathematical answer in the framework of general affine transforms, and holds for several other distributions including heavy-tailed ones.
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Hürlimann, W. General affine transform families: why is the Pareto an exponential transform?. Statistical Papers 44, 499–518 (2003). https://doi.org/10.1007/BF02926007
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DOI: https://doi.org/10.1007/BF02926007