We present a simulation tool based on the Multicanonical Monte Carlo (MMC) method to characterize the statistical properties of bit patterning in semiconductor optical amplifiers (SOAs). Our tool estimates the conditional probability density functions (PDFs) of marks and spaces of the received signal. We introduce an experimental technique to directly measure the conditional PDFs of the received marks and spaces using a high bandwidth sampling scope. We demonstrate that predictions from our simulation tool match the experimental data. We measure the bit error rate (BER) of a SOA-based preamplified receiver, where the SOA operates in the nonlinear regime, and demonstrate that our simulation tool can predict the measured BER.