Abstract
We study a new five-parameter model called the extended Dagum distribution. The proposed model contains as special cases the log-logistic and Burr III distributions, among others. We derive the moments, generating and quantile functions, mean deviations and Bonferroni, Lorenz and Zenga curves. We obtain the density function of the order statistics. The parameters are estimated by the method of maximum likelihood. The observed information matrix is determined. An application to real data illustrates the importance of the new model.
Highlights
The Dagum model pionnered by Camilo Dagum (1977, 1980) has been widely used in studies of income and wealth distributions
We propose a new lifetime model, named the extended Dagum (EDa) distribution with cdf obtained from equation (4) by taking G(x) to be the cdf of the Dagum(β, λ, δ) distribution
These results indicate that the EDa distribution has the lowest Akaike information criterion (AIC) value among all fitted models, and so it could be chosen as the best model
Summary
The Dagum model pionnered by Camilo Dagum (1977, 1980) has been widely used in studies of income and wealth distributions. Domma(2007) derived the asymptotic distribution of the maximum likelihood estimators (MLEs) of the parameters of the right-truncated Dagum ditribution. Several methods for generating new classes of distributions by extending well-known models and at the same time providing great flexibility in modeling real data have been proposed in the last years. For a continuous baseline cdf G(x), Cordeiro et al (2013) defined the exponentiated generalized (“EG”for short) class of distributions by. We propose a new lifetime model, named the extended Dagum (EDa) distribution with cdf obtained from equation (4) by taking G(x) to be the cdf of the Dagum(β, λ, δ) distribution. We obtain some mathematical properties of the new distribution and discuss maximum likelihood estimation of its parameters.
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