An asymmetry-steepness parameterization of the generalized lambda distribution
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.
|Date of creation:||2012|
|Contact details of provider:|| Postal: Ludwigstraße 33, D-80539 Munich, Germany|
Web page: https://mpra.ub.uni-muenchen.de
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Asquith, William H., 2007. "L-moments and TL-moments of the generalized lambda distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4484-4496, May.
- Karvanen, Juha & Nuutinen, Arto, 2008. "Characterizing the generalized lambda distribution by L-moments," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1971-1983, January.
- Su, Steve, 2007. "Numerical maximum log likelihood estimation for generalized lambda distributions," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 3983-3998, May.
- Fournier, B. & Rupin, N. & Bigerelle, M. & Najjar, D. & Iost, A. & Wilcox, R., 2007. "Estimating the parameters of a generalized lambda distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2813-2835, March.
When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:37814. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter)
If references are entirely missing, you can add them using this form.