The Swiss Re Exposure Curves and the MBBEFD Distribution Class

A new two-parameter family of analytical functions would be introduced for the modeling of loss distributions and exposure curves The curve family contains the Maxwell-Boltzmann, the Bose-Einstein and the Fermi-Dirac distributions, which are well known in statistical mechanics. The functions can be used for the modeling of loss distributions on the finite Interval ---- as well as on the interval ----. The functions defined on the interval ---- are discussed in detail and related to several Swiss Re-exposure curves used in practice The curves can be fitted to the first two moments -- and -- of a loss distribution or to the first moment -- and the total loss probability p.