Are the discretised lognormal and hooked power law distributions plausible for citation data?

There is no agreement over which statistical distribution is most appropriate for modelling citation count data. This is important because if one distribution is accepted then the relative merits of different citation-based indicators, such as percentiles, arithmetic means and geometric means, can be more fully assessed. In response, this article investigates the plausibility of the discretised lognormal and hooked power law distributions for modelling the full range of citation counts, with an offset of 1. The citation counts from 23 Scopus subcategories were fitted to hooked power law and discretised lognormal distributions but both distributions failed a Kolmogorov–Smirnov goodness of fit test in over three quarters of cases. The discretised lognormal distribution also seems to have the wrong shape for citation distributions, with too few zeros and not enough medium values for all subjects. The cause of poor fits could be the impurity of the subject subcategories or the presence of interdisciplinary research. Although it is possible to test for subject subcategory purity indirectly through a goodness of fit test in theory with large enough sample sizes, it is probably not possible in practice. Hence it seems difficult to get conclusive evidence about the theoretically most appropriate statistical distribution.

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