Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/123438
Authors: 
Kleiber, Christian
Year of Publication: 
2012
Series/Report no.: 
WWZ Discussion Paper 2012/15
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.
Subjects: 
Generalized error distribution
generalized lognormal distribution
lognormal distribution
moment problem
size distribution
Stieltjes class
volatility model
JEL: 
C46
C02
Document Type: 
Working Paper

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