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The Generalized Lognormal Distribution and the Stieltjes Moment Problem

Christian Kleiber

Working papers from Faculty of Business and Economics - University of Basel

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.

Keywords: Generalized error distribution; generalized lognormal distribution; lognormal distribution; moment problem; size distribution; Stieltjes class; volatility model (search for similar items in EconPapers)
JEL-codes: C46 C02 (search for similar items in EconPapers)
Date: 2012-12-01
New Economics Papers: this item is included in nep-ecm and nep-ets
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Citations: View citations in EconPapers (2) Track citations by RSS feed

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