Price's square root law: Empirical validity and relation to Lotka's law

Abstract Price's well-known square root law states that half of the literature on a subject will be contributed by the square root of the total number of authors publishing in that area. Price's contention is treated here as a hypothesis and assessed against the evidence presented by both empirical and simulated author productivity distributions. The results do not support the square root hypothesis. The problem with Price's original claim is traced to its basis in Lotka's law, which is considered as an inverse square law rather than as a generalized model taking variable parameter values. Varying parameter values engender a family of related, but systematically different, distributions in which the nature of inequality in publication productivity, including the size and relative contribution of the most prolific subset of authors, also varies.

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