Application of the Distribution of Citations Among Publications in Scientometric Evaluations

The pi-indicator (or pi(v)-indicator) of a set of journal papers is equal to a hundredth of the total number of citations obtained by the elite set of publications. The number of publications in the elite set P(pi) is calculated as the square root of total papers. For greater sets the following equation is used: P(pi(v))=(10 log P) - 10, where P is the total number of publications. For sets comprising a single or several extreme frequently cited paper, the pi-index may be distorted. Therefore, a new indicator based on the distribution of citations is suggested. Accordingly, the publications are classified into citation categories, of which lower limits are given as 0, and (2(n) + 1), whereas the upper limits as 2(n) (n = 0, 2, 3, etc.). The citations distribution score (CDS) index is defined as the sum of weighted numbers of publications in the individual categories. The CDS-index increases logarithmically with the increasing number of citations. The citation distribution rate indicator is introduced by relating the actual CDS-index to the possible maximum. Several size-dependent and size-independent indicators were calculated. It has been concluded that relevant, already accepted scientometric indicators may validate novel indices through resulting in similar conclusions ("converging validation of indicators").