One of the major drawbacks of OFDM systems is the notoriously high peak-to-average-power-ratio (PAPR). In this paper we study the performance of a novel PAPR reduction scheme proposed recently, namely Adaptive Dynamic Range Companding (ADRC) by jointly considering the effect of baseband and RF non-linearity. Assuming the baseband OFDM signal as complex Gaussian process, we first derive the exact distribution in a dynamically companded OFDM system. The statistical characteristics of the companded OFDM signal are studied to demonstrate the relationship between the companding parameter and PAPR. The analysis offers theoretical insight into the PAPR reduction and power control.