Chalabi, Yohan and Scott, David J and Wuertz, Diethelm (2012): Flexible distribution modeling with the generalized lambda distribution.
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Abstract
We consider the use of the generalized lambda distribution (GLD) family as a flexible distribution with which to model financial data sets. The GLD can assume distributions with a large range of shapes. Analysts can therefore work with a single distribution to model almost any class of financial assets, rather than needing several. This becomes especially useful in the estimation of risk measures, where the choice of the distribution is crucial for accuracy. We introduce a new parameterization of the GLD, wherein the location and scale parameters are directly expressed as the median and interquartile range of the distribution. The two remaining parameters characterize the asymmetry and steepness of the distribution. Conditions are given for the existence of its moments, and for it to have the appropriate support. The tail behavior is also studied. The new parameterization brings a clearer interpretation of the parameters, whereby the distribution's asymmetry can be more readily distinguished from its steepness. This is in contrast to current parameterizations of the GLD, where the asymmetry and steepness are simultaneously described by a combination of the tail indices. Moreover, the new parameterization can be used to compare data sets in a convenient asymmetry and steepness shape plot.
Item Type:  MPRA Paper 

Original Title:  Flexible distribution modeling with the generalized lambda distribution 
Language:  English 
Keywords:  Quantile distributions; Generalized lambda distribution; Shape plot representation 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General 
Item ID:  43333 
Depositing User:  Yohan Chalabi 
Date Deposited:  20 Dec 2012 12:05 
Last Modified:  28 Sep 2019 02:18 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/43333 
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An asymmetrysteepness parameterization of the generalized lambda distribution. (deposited 03 Apr 2012 12:42)
 Flexible distribution modeling with the generalized lambda distribution. (deposited 20 Dec 2012 12:05) [Currently Displayed]