Loss Models: From Data to Decisions, 4th Edition

E.2 Mean preserving

This method ensures that the discretized distribution has the same mean as the original severity distribution. With no modifications, the discretization is

For the modified distribution.

To incorporate truncation from above, change the denominators to

and subtract h[1 − F_X(u)] from the numerators of each of g₀ and g_(u-d)/h.