A 2-channel data acquisition and processing system (DAPS) for partial discharges PD has been developed. It features a fast (20MSa/sec) digitizer and can acquire up to 16 million samples per channel, yielding an array (qi,(pi), where the qi are the pulse heights of the PDs and the (pi are the corresponding phases. The resolution of this system is 50 mV in pulse height PH and 1°in phase. A 3D plot of the n(qi,(p) is also generated. The statistical package generates the two parameters J3, P2 from the first four moments of the measured PH distributions n(qi), which depend on the total sample size N, and the size of the voltage window AV. A gaussian white noise source was used to generate an artificial PH array Vi for various values ofN and these arrays were input into the data processing part of the system as a test. It was found that for large N (10000) that the Pi, P2 approach the theoretical limit of (0,3) for a normal distribution as expected. Using standard formulas, which map the parameters governing a given distribution into P1, P2 space; similar random PH arrays Vi have been generated for a number of other distributions which map into more extensive regions of Pi, P2 space. These new PH arrays were fed into the data processing part of the system to generate the corresponding Pi, P2 for various values of N and AV as was done for the normal distribution. The new distributions include the Beta, the Gamma, the lognormal, and the Weibull; convergence to the theoretical limits for P1, P2 was again found for large N. However there is an overlap in P1, f3 space for the Beta and Weibull distributions; strategies to overcome the lack of uniqueness will be discussed.