This paper describes the development of a distributed estimation algorithm for amplify-and-forward sensor transmissions with realistic nonlinear amplifier models at the sensors. Specifically, an algorithm is developed that enables distributed estimation with amplifiers operating in the non-linear class AB region. In this system, a digital predistortion scheme is utilized to fit an amplifier to a mathematically tractable, known nonlinearity that is close to the compression characteristics of the amplifier. We show using this scheme has two benefits over linear amplifier operation: improved transmitter efficiency and reduced sensitivity to heavy-tailed distributions due to the soft saturation. The amplifier characteristics and predistortion methods are presented as part of the Java-DSP software package.