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In the present paper, we give su¢ cient conditions for an ordering of De Pril approximations of the distribution of the number of claims in an insurance portfolio of independent policies. Possible extensions are discussed, both for the De Pril approximation and the Kornya approximation. A numerical example is given.doi:10.2139/ssrn.1393713 fatcat:eycb6cuoffemni6kzuseiwxmq4