AbstractAs an alternative method to fractionating the polymer into portions of different molecular weight, in order to obtain the distribution of molecular weights, the method of fitting by statistical moments is proposed. It is shown how from a knowledge of differen order, utilising the inequalities between such averages and their relation to the dispersion of molecular weight, estimates of the distribution function can be obtained: (A) under the assumption of a standard form for the distribution function; (B) without such an assumption, but building up the approximation from a standard form as the norm function and its derivatives; (C) without using any standard form of distribution at all. Numerical examples of the fitting procedures accompany the exposition.