Cosine Fréchet Loss Distribution: Properties, Actuarial Measures and Insurance Applications

Document Type : Original Article

Authors

1 Institute for Basic Sciences, Technology and Innovation. Pan African University, Nairobi, Kenya

2 School of Mathematics, Statistics and Actuarial Science Division, University of Nairobi, Kenya

3 Department of Statistics and Actuarial Science, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

Abstract

In this paper, the cosine Fréchet loss distribution is proposed as a modified version of the Fréchet using the cosine F-Loss generator. The statistical properties and actuarial measures are studied. The maximum likelihood estimators are studied and simulations carried out to ascertain the behavior of the estimators. It is observed that the estimators are consistent. The plots of density show decreasing and right-skewed shapes. The plots of the hazard rate function show reversed-J, increasing-constant-decreasing, bathtub, and upside-down bathtub shapes. From the skewness and kurtosis plots, the skewness is always positive and the kurtosis is increasing. The numerical values of the actuarial measures show that increasing confidence levels are associated with increasing VaR, TVaR, and TV, which is evident in the VaR, TVaR and TV plots. The usefulness of the proposed distribution is demonstrated with two insurance loss datasets. The performance of the CFrL distribution is compared with other known classical heavy-tailed distributions. The results showed that the proposed distribution provides the best parametric fit to the two insurance loss datasets.

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