The Generalized Lognormal Distribution and the Stieltjes Moment Problem
| Autor: | Christian Kleiber |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
FOS: Computer and information sciences Stieltjes class Stieltjes moment problem General Mathematics ARCH-Modell generalized lognormal distribution jel:C46 jel:C02 Shape parameter Generalized error distribution size distribution FOS: Mathematics ddc:330 Applied mathematics volatility model Generalized error distribution generalized lognormal distribution lognormal distribution moment problem size distribution Stieltjes class volatility model Primary 60E05 Secondary 44A60 Generalized normal distribution Mathematics Immobilienpreis Other Statistics (stat.OT) Probability (math.PR) lognormal distribution Statistische Verteilung Riemann–Stieltjes integral Börsenkurs Volatilität Moment problem Statistics - Other Statistics Bounded function Log-normal distribution C46 C02 moment problem Statistics Probability and Uncertainty Random variable Theorie Mathematics - Probability |
| Popis: | 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. 12 pages, 1 figure |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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