Chalabi, Yohan / Y. and Scott, David J and Wuertz, Diethelm (2012): An asymmetrysteepness parameterization of the generalized lambda distribution.
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Abstract
The generalized lambda distribution (GLD) is a versatile distribution that can accommodate a wide range of shapes, including fattailed and asymmetric distributions. It is defined by its quantile function. We introduce a more intuitive parameterization of the GLD that expresses the location and scale parameters directly as the median and interquartile range of the distribution. The remaining two shape parameters characterize the asymmetry and steepness of the distribution respectively. This is in contrasts to the previous parameterizations where the asymmetry and steepness are described by the combination of the two tail indices. The estimation of the GLD parameters is notoriously difficult. With our parameterization, the fitting of the GLD to empirical data can be reduced to a twoparameter estimation problem where the location and scale parameters are estimated by their robust sample estimators. This approach also works when the moments of the GLD do not exist. Moreover, the new parameterization can be used to compare data sets in a convenient asymmetry and steepness shape plot. In this paper, we derive the new formulation, as well as the conditions of the various distribution shape regions and moment conditions. We illustrate the use of the asymmetry and steepness shape plot by comparing equities from the NASDAQ100 stock index.
Item Type:  MPRA Paper 

Original Title:  An asymmetrysteepness parameterization of 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 > C16  Specific Distributions 
Item ID:  37814 
Depositing User:  Yohan Chalabi 
Date Deposited:  03. Apr 2012 12:42 
Last Modified:  19. Feb 2013 06:14 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/37814 
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