On k-distorted generalized discrete family of distributions

ABSTRACT

We propose a new generalized discrete family of distributions which permits inflation/deflation at any single point in the support of distribution. Using the same, a zero-distorted generalized discrete family of distributions is introduced and some of its properties are studied. As an illustration, we study in detail, zero-distorted generalized Poisson distribution. Real-life applications of this distribution using well-known data sets are reported, which include an actuarial application of the proposed model.

KEYWORDS:

• Aggregate loss modeling
• k-distortion
• maximum likelihood function
• Poisson distribution
• zero distortion

Acknowledgments

The authors are thankful to the referees for their constructive comments which have significantly improved several aspects of the paper.

Funding

The first author would like to acknowledge the support of University Grants Commission, New Delhi, under Special Assistance Programme.