Modeling heavy-tailed, skewed and peaked uncertainty phenomena with bounded support
- 192 Downloads
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.
KeywordsUncertainty modeling Applied probability Income distribution Lorentz curve
Unable to display preview. Download preview PDF.
- Kotz S, Johnson NL (1985) Moment ratio diagrams, In: Encyclopedia of statistical sciences, vol 5. Wiley, New YorkGoogle Scholar
- Lévy P (1925) Calcul des probabilitiés, 2nd part, Chap. VI. Gauthier-Villars, ParisGoogle Scholar
- McFall Lamm Jr R (2003) Asymmetric returns and optimal hedge fund portfolios. J Alternat Invest, pp 9–21Google Scholar
- McCulloch J (1996) Financial applications of stable distributions. In: Madfala G, Rao CR (eds) Statistical methods in finance. Elsevier, Amsterdam, pp 393–425Google Scholar
- Pareto V (1964) Cours d’Économie Politique: Nouvelle édition par G.-H. Bousquet et G. Busino. Librairie Droz, Geneva 299–345Google Scholar
- Samorodnitsky G, Taqqu M (2004) Stable non-Gaussian random processes. Chapman & Hall, New YorkGoogle Scholar
- Sarabia JM (2008) Parametric Lorenz curves: models and applications, Modeling Income Distributions and Lorenz Curves. Economic studies in inequality. In: Chotikapanich D (eds) Social exclusion and well-being vol 4. Springer, Berlin, pp 167–190Google Scholar
- Solomon S, Levy M (2000) Market ecology, Pareto wealth distribution and leptokurtic returns in microscopic simulation of the LLS stock market model. In: Proceedings of complex behavior in economics, Aix en Provence (Marseille), France, May 4–6Google Scholar
- Stuart A, Ord JK (1994) Kendall’s advanced theory of statistics. Wiley, New YorkGoogle Scholar