Risk measure estimation under two component mixture models with trimmed data

ABSTRACT

Several two component mixture models from the transformed gamma and transformed beta families are developed to assess risk performance. Their common statistical properties are given and applications to real insurance loss data are shown. A new data trimming approach for parameter estimation is proposed using the maximum likelihood estimation method. Assessment with respect to Value-at-Risk and Conditional Tail Expectation risk measures are presented. Of all the models examined, the mixture of inverse transformed gamma-Burr distributions consistently provides good results in terms of goodness-of-fit and risk estimation in the context of the Danish fire loss data.

KEYWORDS:

• Danish fire loss data
• heavy tailed distributions
• mixture models
• transformed gamma and transformed beta families

Acknowledgments

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

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

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