We describe a statistical model of the power gain patterns of a set of planar antennas, randomly generated from a starting parameterized design. It is first based on a spherical harmonics and double Fourier series expansion for each antenna pattern, followed by the statistical model of the expansion coefficients over the full set. This double compression method results in only a few tens of parameters to reconstruct all patterns. The method fails at the poles when it is applied to a polarization component of the pattern but this does not appear to be a critical problem.