Stationary scientometric distributions

It is formulated that the use of non-Gaussian statistics is necessary in the science of science and other social sciences because the sample moments appear to depend significantly on the sample size.

Abstract

Stationary distributions, i.e. distributions involving no time dependence, are considered. It is shown that all these distributions in scientometrics can be approximated by the Zipf distribution at high values of variables. The sample moments appear to depend significantly on the sample size. Accordingly, the approximation of these observational data by probability distributions converging to a stable distribution different from the normal one proves to be the only correct approximation. The conclusion is formulated that the use of non-Gaussian statistics is necessary in the science of science and other social sciences.