Self-oscillating power amplifiers (SOPA) are promising solutions for amplification of high crest factor signals, with good linearity and efficiency, as a result of using a switch mode amplifier inside the oscillating loop. The lack of comprehensive and statistical analysis method complicates the design and analysis procedure. In this paper, a new statistical approach is presented to analyze the nonlinear behavior of SOPA, to predict the required system metrics like EVM and ACPR. The approach is an extension to the describing function concept and is suitable for a general class of complex Gaussian input signals. The approach is validated through comparison with transistor level simulations and measurements performed on a single chip SOPA realized in 65 nm CMOS technology, for three types of input signal.