Note Concerning the Distribution Function of the Total Loss Excluding the Largest Individual Claims

The theory of extreme values is a special branch of mathematmalstahstms and was mainly treated by E J Gumbel [4] *) This theory has only been apphed m a few cases to problems m the Insurance business The first practmal apphcatlon to insurance known to the author of the present paper is due to A Th6paut who has Invented a new reinsurance system called ECOMOR [5] According to this system the reinsurer covers the excess a s k for the m largest claims and the ceding company retains an amount
equal to the (m + i) largest clam1 The credit for having pointed out the Importance of the theory of extreme values belongs to R E Beard [x] Recently E Franckx [3] has found a most remark-able result by disclosing the general form of the distnbutlon for the largest claim occurring In a certain accounting period