In this work, we present a complete numerical simulation of a light emitting diode based on the alloys AlGaN and InGaN. Using material parameters obtained from the literature, a good comparison between numerical simulations and experiments can be achieved. For high brightness in these devices, we would like to have most of the recombination taking place at the dopants in the active region of the device. However, if this region is not doped high enough, we observe that the output power will be saturated. This therefore also gives us a method for finding the concentration of dopants in the active region.