A family of density-hazard distributions for insurance losses

Abstract

We propose a family of distributions as an alternative for a recent compound unimodal distribution for modeling insurance losses. The family of distributions, referred to as density-hazard distributions, has closed form density and distribution functions, hence easier to fit and simulate from. The distributions also show good adherence to insurance loss data and estimates risk measures relatively closely to the empirical values. In this respect, the practical use of the density-hazard distributions is demonstrated with the employment of three real insurance data including the U.S. indemnity insurance loss data, the U.S. automobile claims data, and the Norwegian fire losses data.

KEYWORDS:

• Compound unimodal distributions
• Heavy tailed distributions
• Insurance losses
• Risk measures

Acknowledgment

The authors would like to thank the Editor and the two referees for careful reading and comments which greatly improved the paper.

Additional information

Funding

This work has been supported by the Ministry of Higher Education, Malaysia under Fundamental Research Grant Scheme (FRGS) FP040-2017A.