[Sigmetrics] Lotka's Law Reverse-Engineered
Stephen J Bensman
notsjb at lsu.edu
Wed Jan 20 10:24:51 EST 2016
My colleague, Lawrence Smolinsky, and I have reverse-engineered Lotka's inverse square law of scientific productivity to determine precisely how he derived this famous law. He did this by basing the derivation of his law on the method of identifying power-law behavior by the R^2 fit to a regression line on a log-log plot that modern theory considers unreliable. We have found that Lotka's law should really be renamed Lotka's Inverse Square Power Law of Scientific Productivity with Exponential Cut-Off in today's lingo. Lotka himself suspected this but could not prove it because his data was so censored on the right due to small samples that he considered it necessary to severely truncate it there.
As I grow older, I become more curmudgeonly and enjoy doing things like this.
Stephen J Bensman
LSU Libraries (Retired)
Lousiana State University
Baton Rouge, LA 70803
Our proof is in the two pieces below that we just have posted on arXiv. If you have any bitches, please let me know.:
Lotka's Inverse Square Law of Scientific Productivity: Its Methods and Statistics
Authors: Stephen J. Bensman<http://arxiv.org/find/cs/1/au:+Bensman_S/0/1/0/all/0/1>, Lawrence J. Smolinsky<http://arxiv.org/find/cs/1/au:+Smolinsky_L/0/1/0/all/0/1>
(Submitted on 19 Jan 2016)
Abstract: This brief communication analyzes the statistics and methods Lotka used to derive his inverse square law of scientific productivity from the standpoint of modern theory. It finds that he violated the norms of this theory by extremely truncating his data on the right. It also proves that Lotka himself played an important role in establishing the commonly used method of identifying power-law behavior by the R^2 fit to a regression line on a log-log plot that modern theory considers unreliable by basing the derivation of his law on this very method.
12 pages, 5 figures, 2 tables
Digital Libraries (cs.DL)
(or arXiv:1601.04950v1<http://arxiv.org/abs/1601.04950v1> [cs.DL] for this version)
Discrete power law with exponential cutoff and Lotka's Law
Authors: Lawrence Smolinsky<http://arxiv.org/find/cs/1/au:+Smolinsky_L/0/1/0/all/0/1>
(Submitted on 29 Dec 2015)
Abstract: The first bibliometric law appeared in Alfred J. Lotka's 1926 examination of author productivity in chemistry and physics. The result is that the productivity distribution is thought to be described by a power law. In this paper, Lotka's original data on author productivity in chemistry is reconsidered by comparing the fit of the data to both a discrete power law and a discrete power law with exponential cutoff.
Digital Libraries (cs.DL); Data Analysis, Statistics and Probability (physics.data-an)
(or arXiv:1512.08754v1<http://arxiv.org/abs/1512.08754v1> [cs.DL] for this version)
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