A characterization of scientometric distributions based on harmonic means
The traditional stochastic approach to scientometric and bibliometric phenomena is based on measuring the absolute number of objects (e.g., publications, topics, citations). These measures reflect underlying rules such as the cumulative advantage principle and lead to classical statistical functions such as arithmetic mean and standard deviation. An alternative measure based on the contribution share of an individual object in the entirety of related objects reveals more about the coherence in the analyzed structure. This approach is connected with (conditional) harmonic means. The analysis of the properties of these statistical functions leads to a special urn-model distribution which has an analogous behaviour to that of the Waring distribution in connection with conditional arithmetic means. The new distribution combines specific properties (long tail, flexibility of the distribution shape) of the two scientometric favourites, the Waring and the negative binomial distribution. Five methods of parameter estimation are presented. The fit and the properties of this special urn-model distribution are illustrated by three scientometric examples, particularly, by two citation rate distributions with different shapes and one publication activity distribution with lacking zero frequencies.
KeywordsCoherence Absolute Number Binomial Distribution Statistical Function Alternative Measure
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