Probabilities for encountering genius, basic, ordinary or insignificant papers based on the cumulative nth citation distribution

Abstract

This article calculates probabilities for the occurrence of different types of papers such as genius papers, basic papers, ordinary papers or insignificant papers. The basis of these calculations are the formulae for the cumulative n-th citation distribution, being the cumulative distribution of times at which articles receive their n-th (n=1,2,3,...) citation. These formulae (proved in previous papers) are extended to allow for different aging rates of the papers. These new results are then used to define different importance classes of papers according to the different values of n, in function of time t. Examples are given in case of a classification into four parts: genius papers, basic papers, ordinary papers and (almost) insignificant papers. The fact that, in these examples, the size of each class is inversely related to the importance of the journals in this class is proved in a general mathematical context in which we have an arbitrary number of classes and where the threshold values of n in each class are defined according to the natural law of Weber-Fechner.