The exponentiated Fréchet regression: an alternative model for actuarial modelling purposes. (English) Zbl 07184809
Summary: 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.
MSC:
| 62J05 | Linear regression; mixed models |
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
Keywords:
exponentiated Gumbel distribution; generalized Fréchet distribution; maximum likelihood estimation; regression modelling; risk measuresReferences:
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