AbstractIt is of considerable practical importance to be able to describe the distribution of molecular sizes of a polymeric material by a convenient mathematical expression. Since the various molecular averages of any distribution are obtained from a summation process, the general models require an analytical expression of the differential distribution and a corresponding definite integral generally having the integration limits of zero and infinity. In general, real polymer distributions do not fit these integration limits and an error, which can be very large, is therefore introduced. If the error in the various molecular weight averages due to changes in integration limits is of the order of or less than the error generally encountered in the experimental evaluation of the average, the distribution function can be considered to be applicable from a practical point of view. In addition, the selected model should fulfill the requirements of fitting known experimental facts such as: the polymerization kinetics, the effects of random degradation and crosslinking, fractionation data, and the effects of polymerization and processing on the differential distribution maxima. It should also conform to the rheological behavior based on current theoretical ideas. The integration limit criteria are applied to logarithmic normal type distributions, e.g., Wesslau, and generalized exponential type distributions, e.g., Schulz‐Zimm and Tung. The results show that logarithmic normal type distributions cannot be considered as useful models, while the generalized exponential type distributions can be valid and useful representations.