Chalabi, Yohan / Y. and Scott, David J and Wuertz, Diethelm (2012): An asymmetry-steepness parameterization of the generalized lambda distribution.
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The generalized lambda distribution (GLD) is a versatile distribution that can accommodate a wide range of shapes, including fat-tailed 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 inter-quartile 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 two-parameter 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 NASDAQ-100 stock index.
|Item Type:||MPRA Paper|
|Original Title:||An asymmetry-steepness parameterization of the generalized lambda distribution|
|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|
|Depositing User:||Yohan Chalabi|
|Date Deposited:||03. Apr 2012 12:42|
|Last Modified:||19. Feb 2013 06:14|
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