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The Generalized Lognormal Distribution and the Stieltjes Moment Problem

Kleiber, Christian. (2012) The Generalized Lognormal Distribution and the Stieltjes Moment Problem. WWZ Discussion Papers, 2012 (15).

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Abstract

This paper studies a Stieltjes-type moment problem defined by the generalized lognormal distribution, a heavy-tailed distribution with applications in economics, finance and related fields. It arises as the distribution of the exponential of a random variable following a generalized error distribution, and hence figures prominently in the EGARCH model of asset price volatility. Compared to the classical lognormal distribution it has an additional shape parameter. It emerges that moment (in)determinacy depends on the value of this parameter: for some values, the distribution does not have finite moments of all orders, hence the moment problem is not of interest in these cases. For other values, the distribution has moments of all orders, yet it is moment-indeterminate. Finally, a limiting case is supported on a bounded interval, and hence determined by its moments. For those generalized lognormal distributions that are moment-indeterminate Stieltjes classes of moment-equivalent distributions are presented.
Faculties and Departments:06 Faculty of Business and Economics > Departement Wirtschaftswissenschaften > Professuren Wirtschaftswissenschaften > ├ľkonometrie und Statistik (Kleiber)
12 Special Collections > WWZ Publications > WWZ Discussion Papers and Working Papers
UniBasel Contributors:Kleiber, Christian
Item Type:Working Paper
Publisher:WWZ, University of Basel
Number of Pages:14
Note:Publication type according to Uni Basel Research Database: Discussion paper / Internet publication
Language:English
Identification Number:
  • handle: RePEc:bsl:wpaper:2012/15
Last Modified:16 Mar 2018 15:12
Deposited On:08 Mar 2018 13:24

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