Proceedings of the 1st International Conference on Bilbliometrics and Information Retrieval location:Diepenbeek (Belgium) date:24-28 August 1987
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 (1-F(k))*k^alpha = const for some real alpha > 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, alpha, 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 alpha as well as statistical tests for extreme values and ranked tail elements are developed. The methods are illustrated on empirical samples of citation rates and publication activity.