On the Use of Equispaced Discrete Distributions

The Kolmogorov distance is used to transform arithmetic severities into equispaced arithmetic severities in order to reduce the number of calculations when using algorithms like Panjer's formulae for compound distributions. An upper bound is given for the Kolmogorov distance between the true compound distribution and the transformed one. Advantages of the Kolmogorov distance and disadvantages of the total variation distance are discussed. When the bounds are too big, a Berry-Esseen result can be used. Then almost every case can be handled by the techniques described in this paper. Numerical examples show the interest of the methods. Keywords: Recursive formula; compound distribution; infinite divisibility; equispaced discrete distribution; Koimogorov distance; total variation distance; upper and lower bounds; Berry-Esseen bound.