The beta generalized gamma distribution

Abstract

For the first time, a new five-parameter distribution, called the beta generalized gamma distribution, is introduced and studied. It contains at least 25 special sub-models such as the beta gamma, beta Weibull, beta exponential, generalized gamma (GG), Weibull and gamma distributions and thus could be a better model for analysing positive skewed data. The new density function can be expressed as a linear combination of GG densities. We derive explicit expressions for moments, generating function and other statistical measures. The elements of the expected information matrix are provided. The usefulness of the new model is illustrated by means of a real data set.

Keywords:

• beta generalized distribution
• expected information matrix
• generalized gamma distribution
• mean deviation
• moment

Acknowledgements

The authors thank the two referees for their very useful comments. G.M. Cordeiro and M. Castro were partially supported by, respectively, CNPq, Brazil, and FAPESP, Brazil. F. Castellares and L.C. Montenegro were partially supported by FAPEMIG, Brazil.