We find that the distributions depart significantly from a Gaussian shape mainly in regions of large-scale descent. This non-Gaussianity is associated with significant positive skewness. The Gamma and the Log-Normal distributions have been widely used to describe positively skewed precipitation distributions. We find, however, that both are poor fits to the observed seasonal mean precipitation distributions at many locations around the globe. Both also fail to account for the frequency of no precipitation, a quantity of vital economic interest in many regions of the world. The Gamma fit is poor in regions of strong descent. The Log-Normal fit is poor in regions of strong descent and also of strong ascent, where the observed distributions are largely Gaussian. Comparisons among the precipitation datasets show that the results of this study are robust to the choice of dataset.