On the Harris extended family of distributions

Abstract

A new method for generating new classes of distributions based on the probability-generating function is presented in Aly and Benkherouf [A new family of distributions based on probability generating functions. Sankhya B. 2011;73:70–80]. In particular, they focused their interest to the so-called Harris extended family of distributions. In this paper, we provide several general results regarding the Harris extended models such as the general behaviour of the failure rate function. We also derive a very useful representation for the Harris extended density function as an absolutely convergent power series of the survival function of the baseline distribution. Additionally, some stochastic order relations are established and limiting distributions of sample extremes are also considered for this model. These general results are illustrated in several special Harris extended models. Finally, we discuss estimation of the model parameters by the method of maximum likelihood and provide an application to real data for illustrative purposes.

Keywords:

• distributions of sample extremes
• Harris extended distributions
• Marshall–Olkin extended distributions
• maximum likelihood estimation
• moments
• stochastic orders

Mathematics Subject Classification:

• 60E05
• 62E15
• 62F10

Acknowledgements

We are grateful to the referees for the comments and suggestions, as well as their general positiveness.

Funding

Artur Lemonte gratefully acknowledges financial support from CNPq (Brazil) and FACEPE (Pernambuco, Brazil).