Abstract
This paper considers a generalized four parameter statistical distribution as a model of losses, the generalized beta of the second kind (GB2). The distribution is very flexible and can model positive as well as negatively skewed data and also provides a model for thick and thin tailed distributions. The distribution provides an important structural interpretation in that it can accommodate unobservable heterogeneity. Heterogeneity is not imposed, but is accommodated by the model. The distribution includes such other important models encountered in the insurance literature as the lognormal, gamma, exponential, log-t and Burr distributions as special and limiting cases. Van der Laan [1987] provides a brief but excellent historical survey of a number of common distributions in modeling losses in insurance. Hogg and Klugman [1984] contains a careful development of alternative models and a treatment of estimation and inferential questions arising with loss distributions. The stable family of distributions has been considered by Paulson and Fair [1985].
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McDonald, J.B. (1991). Some Statistical Distributions for Insured Damages. In: Cummins, J.D., Derrig, R.A. (eds) Managing the Insolvency Risk of Insurance Companies. Huebner International Series on Risk, Insurance, and Economic Security, vol 12. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3878-9_7
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DOI: https://doi.org/10.1007/978-94-011-3878-9_7
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