  We consider a version of D. Price's model for the growth of a bibliographic
network, where in each iteration a constant number of citations is randomly
allocated according to a weighted combination of accidental (uniformly
distributed) and preferential (rich-get-richer) rules. Instead of relying on
the typical master equation approach, we formulate and solve this problem in
terms of the rank-size distribution. We show that, asymptotically, such a
process leads to a Pareto-type 2 distribution with an appealingly interpretable
parametrisation. We prove that the solution to the Price model expressed in
terms of the rank-size distribution coincides with the expected values of order
statistics in an independent Paretian sample. We study the bias and the mean
squared error of three well-behaving estimators of the underlying model
parameters. An empirical analysis of a large repository of academic papers
yields a good fit not only in the tail of the distribution (as it is usually
the case in the power law-like framework), but also across the whole domain.
Interestingly, the estimated models indicate higher degree of preferentially
attached citations and smaller share of randomness than previous studies.
