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Modeling heavy-tailed, skewed and peaked uncertainty phenomena with bounded support

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Abstract

A prevalence of heavy-tailed, peaked and skewed uncertainty phenomena have been cited in literature dealing with economic, physics, and engineering data. This fact has invigorated the search for continuous distributions of this nature. In this paper we shall generalize the two-sided framework presented in Kotz and van Dorp (Beyond beta: other continuous families of distributions with bounded support and applications. World Scientific Press, Singapore, 2004) for the construction of families of distributions with bounded support via a mixture technique utilizing two generating densities instead of one. The family of Elevated Two-Sided Power (ETSP) distributions is studied as an instance of this generalized framework. Through a moment ratio diagram comparison, we demonstrate that the ETSP family allows for a remarkable flexibility when modeling heavy-tailed and peaked, but skewed, uncertainty phenomena. We shall demonstrate its applicability via an illustrative example utilizing 2008 US income data.

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Authors and Affiliations

  1. Departamento de Métodos Cuantitativos para la Economía y la Empresa, Facultad de Ciencias Económicas y Empresariales, University of Granada, Campus de Cartuja s/n, Granada, 18071, Spain

    C. B. García

  2. Departamento de Economía Aplicada, University of Almería, Ctra. La Cañada de San Urbano, s/n, Almería, 04120, Spain

    J. García Pérez

  3. Department of Engineering Management and Systems Engineering, The George Washington University, 1776 G Street N.W, Washington, DC, 20052, USA

    J. R. van Dorp

Authors
  1. C. B. García
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  2. J. García Pérez
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  3. J. R. van Dorp
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Correspondence to J. R. van Dorp.

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García, C.B., García Pérez, J. & van Dorp, J.R. Modeling heavy-tailed, skewed and peaked uncertainty phenomena with bounded support. Stat Methods Appl 20, 463–486 (2011). https://doi.org/10.1007/s10260-011-0173-0

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