The exponentiated Fréchet regression: an alternative model for actuarial modelling purposes

ABSTRACT

In this paper we introduce the exponentiated Fréchet regression for modelling positive responses having a long-tailed distribution in a regression model, which are common in actuarial statistics. We propose two parameterizations each of which links the regression parameters with the explanatory variables. We then discuss the maximum likelihood estimation of the parameters both theoretically and empirically. In order to meet the needs of an actuary, closed-form expressions for certain risk measures for the exponentiated Fréchet distribution are also derived. We employ the proposed model to a motorcycle claim size data set.

KEYWORDS:

• Exponentiated Gumbel distribution
• generalized Fréchet distribution
• maximumlikelihood estimation
• regression modelling
• risk measures

AMS SUBJECT CLASSIFICATION:

• 62J05
• 62P05

Disclosure statement

No potential conflict of interest was reported by the authors.