This paper analyses the statistics of the clipping noise in orthogonal frequency-division-multiplex (OFDM) based visible light Communication systems. The clipped signal is generally modelled as the summation of the scaled original signal and clipping noise, which is treated by the linear equalizer in the receiver. Generally, it is assumed that the clipped and original signal share the same statistics. Although valid in some cases, we show that such assumption is invalid when the transmitter is tightly constrained. We derive closed-form probability distribution function (pdf) for the clipping noise and use the pdf for statistical hypothesis testing in an optimum receiver