An extension of the gamma distribution

ABSTRACT

The gamma distribution has been widely used in many research areas such as engineering and survival analysis. We present an extension of this distribution, called the Kummer beta gamma distribution, having greater flexibility to model scenarios involving skewed data. We derive analytical expressions for some mathematical quantities. The estimation of parameters is approached by the maximum likelihood method and Bayesian analysis. The likelihood ratio and formal goodness-of-fit tests are used to compare the presented distribution with some of its sub-models and non nested models. A real data set is used to illustrate the importance of the distribution.

Keywords:

• Bayesian approach
• Gamma distribution
• Kummer beta generalized distribution
• Maximum likelihood method
• Moment
• Order statistic

MATHEMATICS SUBJECT CLASSIFICATION:

• 60E05
• 62E99

Acknowledgments

The authors would like to thank the editor and the referee for careful reading and for comments which greatly improved the paper.