Generalized beta-generated distributions
This article introduces generalized beta-generated (GBG) distributions. Sub-models include all classical beta-generated, Kumaraswamy-generated and exponentiated distributions. They are maximum entropy distributions under three intuitive conditions, which show that the classical beta generator skewness parameters only control tail entropy and an additional shape parameter is needed to add entropy to the centre of the parent distribution. This parameter controls skewness without necessarily differentiating tail weights. The GBG class also has tractable properties: we present various expansions for moments, generating function and quantiles. The model parameters are estimated by maximum likelihood and the usefulness of the new class is illustrated by means of some real data sets.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
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.:
- John Galbraith & Dongming Zhu, 2009.
"A Generalized Asymmetric Student-T Distribution With Application To Financial Econometrics,"
Departmental Working Papers
2009-02, McGill University, Department of Economics.
- Zhu, Dongming & Galbraith, John W., 2010. "A generalized asymmetric Student-t distribution with application to financial econometrics," Journal of Econometrics, Elsevier, vol. 157(2), pages 297-305, August.
- Dongming Zhu & John Galbraith, 2009. "A Generalized Asymmetric Student-t Distribution with Application to Financial Econometrics," CIRANO Working Papers 2009s-13, CIRANO.
- Brys, Guy & Hubert, Mia & Struyf, Anja, 2006. "Robust measures of tail weight," Computational Statistics & Data Analysis, Elsevier, vol. 50(3), pages 733-759, February.
- M. Jones, 2004. "Families of distributions arising from distributions of order statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 13(1), pages 1-43, June.
- M. C. Jones & P. V. Larsen, 2004. "Multivariate distributions with support above the diagonal," Biometrika, Biometrika Trust, vol. 91(4), pages 975-986, December.
- Hansen, B.E., 1992.
"Autoregressive Conditional Density Estimation,"
RCER Working Papers
322, University of Rochester - Center for Economic Research (RCER).
- Amit Choudhury, 2005. "A Simple Derivation of Moments of the Exponentiated Weibull Distribution," Metrika, Springer, vol. 62(1), pages 17-22, 09.
- Kjersti Aas & Ingrid Hobaek Haff, 2006. "The Generalized Hyperbolic Skew Student's t-Distribution," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(2), pages 275-309.
- Nadarajah, Saralees, 2008. "Explicit expressions for moments of order statistics," Statistics & Probability Letters, Elsevier, vol. 78(2), pages 196-205, February.
- M. C. Jones & M. J. Faddy, 2003. "A skew extension of the "t"-distribution, with applications," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 159-174.
- McDonald, James B, 1984. "Some Generalized Functions for the Size Distribution of Income," Econometrica, Econometric Society, vol. 52(3), pages 647-63, May.
- McDonald, James B. & Xu, Yexiao J., 1995.
"A generalization of the beta distribution with applications,"
Journal of Econometrics,
Elsevier, vol. 69(2), pages 427-428, October.
- McDonald, James B. & Xu, Yexiao J., 1995. "A generalization of the beta distribution with applications," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 133-152.
- Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew "t"-distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389.
- D. Mikis Stasinopoulos & Robert A. Rigby, . "Generalized Additive Models for Location Scale and Shape (GAMLSS) in R," Journal of Statistical Software, American Statistical Association, vol. 23(i07).
- Arnold, Barry C. & Castillo, Enrique & Sarabia, Jose Maria, 2006. "Families of Multivariate Distributions Involving the Rosenblatt Construction," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1652-1662, December.
- Ebrahimi, Nader & Maasoumi, Esfandiar & Soofi, Ehsan S., 1999. "Ordering univariate distributions by entropy and variance," Journal of Econometrics, Elsevier, vol. 90(2), pages 317-336, June.
When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1880-1897. 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: (Zhang, Lei)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.