  Modeling distributions of citations to scientific papers is crucial for
understanding how science develops. However, there is a considerable empirical
controversy on which statistical model fits the citation distributions best.
This paper is concerned with rigorous empirical detection of power-law
behaviour in the distribution of citations received by the most highly cited
scientific papers. We have used a large, novel data set on citations to
scientific papers published between 1998 and 2002 drawn from Scopus. The
power-law model is compared with a number of alternative models using a
likelihood ratio test. We have found that the power-law hypothesis is rejected
for around half of the Scopus fields of science. For these fields of science,
the Yule, power-law with exponential cut-off and log-normal distributions seem
to fit the data better than the pure power-law model. On the other hand, when
the power-law hypothesis is not rejected, it is usually empirically
indistinguishable from most of the alternative models. The pure power-law model
seems to be the best model only for the most highly cited papers in "Physics
and Astronomy". Overall, our results seem to support theories implying that the
most highly cited scientific papers follow the Yule, power-law with exponential
cut-off or log-normal distribution. Our findings suggest also that power laws
in citation distributions, when present, account only for a very small fraction
of the published papers (less than 1% for most of science fields) and that the
power-law scaling parameter (exponent) is substantially higher (from around 3.2
to around 4.7) than found in the older literature.
