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In general insurance, claims are often lower-truncated and right-censoredbecause insurance contracts may involve deductibles and maximal covers. Mostclassical statistical models are not (directly) suited to model lower-truncatedand right-censored claims. A surprisingly flexible family of distributions thatcan cope with lower-truncated and right-censored claims is the class of MBBEFDdistributions that originally has been introduced by Bernegger (1997) forreinsurance pricing, but which has not gained much attention outside thereinsurance literature. We derive properties of the class of MBBEFDdistributions, and we extend it to a bigger family of distribution functionssuitable for modeling lower-truncated and right-censored claims. Interestingly,in general insurance, we mainly rely on unimodal skewed densities, whereas thereinsurance literature typically proposes monotonically decreasing densitieswithin the MBBEFD class.

Modeling lower-truncated and right-censored insurance claims with an extension of the MBBEFD class