Theoretical and empirical studies of the tails of scientometric distributions

Abstract

The distributions of non-negative random variables occurring in scientometrics are said to have a proper tail if they asymptotically obey "Zipf's Law", i.e., if

lim (I-F(k)) k a = const k- "

for some real a > 0 where F denotes the cumulative distribution. The tail of scientometric distributions has a particular significance because it generally contains the most "prominent" elements of the population (e.g. highest cited papers or most productive authors). In addition, the tail parameter, a , is a sensitive indicator of several fundamental features of the whole distribution. It is shown that, among others, the tail parameter governs order and rank statistics. New estimation methods of a as well as statistical tests f w extreme values and ranked tail elements are developed. The methods are illustrated on empirical samples of citation rates and publication activity.