THEORETICAL ANALYSIS OF EMPIRICAL RELATIONSHIPS FOR PARETO- DISTRIBUTED SCIENTOMETRIC DATA

In this paper we study some problems involved in analysis of Pareto-distributed scientometric data (series of citations versus paper ranks). The problems include appropriate choices of i) the distribution type (continuous, discrete or finite-size discrete) and ii) statistical methods to obtain unbiased estimates for the power- law exponent (maximum likelihood procedure or least square regression.). Since relatively low magnitudes of the power exponent (less than 2), are observed massively in scientometric databases, finite-size discrete Pareto distribution (citations, distributed to finite number of paper ranks) appears to be more adequate for data analysis than the traditional ones. This conclusion is illustrated with two examples (for synthetic and actual data, respectively). We also derive empirical relationships, in particular, for the maximum and the total number of citations dependence on the Hirsch index. The latter generalize results of previous studies.