New results on the Ristić–Balakrishnan family of distributions

ABSTRACT

Adding new shape parameters to expand a model into a larger family of distributions to provide significantly skewed and heavy-tails plays a fundamental role in distribution theory. For any continuous baseline G distribution, Ristić and Balakrishnan (2012) proposed the gamma-generated family of distributions with an extra positive shape parameter. They presented some special models of their family but did not study its properties. This paper examines some general mathematical properties of this family which hold for any baseline model. Some distributions are studied and a number of existing results in the literature can be recovered as special cases. We estimate the model parameters by maximum likelihood and illustrate the importance of the family by means of an application to a real data set.

Keywords:

• Gamma distribution
• Generating function
• Maximum likelihood
• Mean deviation
• Moment
• Ristić–Balakrishnan family.

Acknowledgment

We thank the editor and the reviewer again for the constructive comments.