The Generalized Lognormal Distribution and the Stieltjes Moment Problem
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.
|Date of creation:||2012|
|Date of revision:|
|Contact details of provider:|| Postal: Peter-Merian-Weg 6, Postfach, CH-4002 Basel|
Web page: http://wwz.unibas.ch
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Samuel Kotz & Christian Kleiber, 2002. "A characterization of income distributions in terms of generalized Gini coefficients," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(4), pages 789-794.
- Alfarano, Simone & Milaković, Mishael & Irle, Albrecht & Kauschke, Jonas, 2012.
"A statistical equilibrium model of competitive firms,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 36(1), pages 136-149.
- Irle, Albrecht & Milaković, Mishael & Alfarano, Simone & Kauschke, Jonas, 2008. "A Statistical Equilibrium Model of Competitive Firms," Economics Working Papers 2008,10, Christian-Albrechts-University of Kiel, Department of Economics.
When requesting a correction, please mention this item's handle: RePEc:bsl:wpaper:2012/15. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (WWZ)
If references are entirely missing, you can add them using this form.