Abstract
Skewed and fat-tailed distributions frequently occur in many applications. Models proposed to deal with skewness and kurtosis may be difficult to treat because the density function cannot usually be written in a closed form and the moments might not exist. The log-Dagum distribution is a flexible and simple model obtained by a logarithmic transformation of the Dagum random variable. In this paper, some characteristics of the model are illustrated and the estimation of the parameters is considered. An application is given with the purpose of modeling kurtosis and skewness that mark the financial return distribution.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Abberger K (2002) ML-estimation in the location-scale-shape model of the generalized logistic distribution, CoFE Discussion Paper, No. 02-15. http://econpapers.repec.org/paper/knzcofedp/0215.htm
Abberger K, Heiler S (2000) Simultaneous estimation of parameters for a generalized distribution and application to time series models. All Stat Arch 84: 41–49
Arnold BC, Balakrishnan N, Nagaraja HN (1992) A first course in order statistics. Wiley, New York
Cont R (2001) Empirical properties of asset returns: stylized facts and statistical issues. Quant Finance 1: 223–236
Dagum C (1977) A new model for personal income distribution: specification and estimation. Economie Appliquée 30: 413–437
Dagum C (1980) The generation and distribution of income, the Lorenz curve and the Gini ratio. Economie Appliquée 33: 327–367
Domma F (2001) Asimmetrie puntuali e trasformazioni monotone. Quad Stat 3: 145–164
Domma F (2002) L’andamento della hazard function nel modello di Dagum. Quad Stat 4: 103–114
Domma F (2004) Kurtosis diagram for the Log-Dagum distribution. Statistica Applicazioni 2: 3–23
Domma F, Perri PF (2005) Some developments on Log-Dagum distribution. Discussion Paper Series, no. 44, Dipartimento di Economia e Statistica, Università della Calabria. http://www.ecostat.unical.it
Johnson NL, Kotz S, Balakrishnan N (1995) Continuous univariate distributions, vol 2. Wiley, New York
Kleiber C, Kotz S (2003) Statistical size distribution in economics and actuarial sciences. Wiley, Hoboken
McCulloch JH (1996) Financial applications of stable distribution. In: Maddala GS, Rao CR(eds) Handbook of Statistics, vol 14. Elsevier, North-Holland, pp 393–425
McDonald JB, Xu YJ (1995) A generalization of the beta distribution with applications. J Econom 66: 132–152
Rachev S, Mittnik S (2000) Stable paretian models in finance. Wiley, New York
Shao Q (2002) Maximum likelihood estimation for generalized logistic distributions. Commun Stat Theory Methods 31: 1687–1700
Zehna PV (1966) Invariance of maximum likelihood estimation. Ann Math Stat 37: 744–755
Zelterman D (1987) Parameter estimation in the generalized logistic distribution. Comput Stat Data Anal 5: 177–187
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Domma, F., Perri, P.F. Some developments on the log-Dagum distribution. Stat Methods Appl 18, 205–220 (2009). https://doi.org/10.1007/s10260-007-0091-3
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10260-007-0091-3