In this paper we validate through software simulation that a Gamma probability density function (pdf) can give a very good approximation of the detected intensity of the incoherent light source. We performed two experiments, in the first experiment the pdf of 0.25 nm optical signal is measured for different photo detector's electrical bandwidth. In the second experiment the eye diagram reading is performed for the optical signal at 2.5 Gbps. Results show that the simulated pdf and computed pdf agree to very high extent. Results also show that the variance in the received signal for logic '0' is negligible, meanwhile for logic '1' the variance is very large and increases with electrical bandwidth. © 2013 IEEE.