This paper provides on a theoretical and numerical study of the probability density function (PDF) of the on-off keying (OOK) signals in ASE-limited systems. We present simple closed formulas of PDFs for the optical intensity and the received baseband signal. To confirm the validity of our model, the calculation results yielded by the proposed formulas are compared with those of numerical simulations and the conventional Gaussian model. Our theoretical and numerical results confirm that the signal distribution differs from a Gaussian profile. It is also demonstrated that our model can properly evaluate the signal distribution and the resultant BER performance, especially for systems with an optical bandwidth close to the receiver baseband width.