The subject says it all... what's the validity of this, and what would be the best sum method? I am trying it out on a three-parameter Weibull distribution and the sum is leading toward values of 1.4 whereas it should be topping off at 1.

Of course, I then shrunk this Riemann sum to be equal to each point value over the maximum leading to a sum of 1, but this created a bias when I compared the expected values to observed values (generated from simulation via psuedo-random numbers looking up on these Riemann sum values).

Any thoughts from the stats and calc pros out there?