The distribution of scientific productivity and social change

Abstract

Results in the literature concerning the probability that an author publishes r articles in time t are reexamined, and it is found that a negative binomial distribution fits scientific productivity data (by the chi‐squared goodness‐of‐fit test) better than many other distributions such as geometric, logarithmic, zeta, cumulative advantage, etc. It is shown analytically that the negative binomial distribution describes a pattern of scientific productivity under the “success‐breeds‐success” condition in a wide variety of social circumstances.

Estimation of the publication potential in 50 U.S. states and in the District of Columbia based on the frequency distribution of scientific productivity

“…Lack of zero-frequency data causes no problem in applying Equation (3). Only the first point (belonging to s = 0) will be missing, but this raises no difficulties in using either the test or the parameter estimation.…”

“…A considerable part of this literature proposed and tested various theoretical models of the productivity distribution. Several of them were comparatively assessed by Rao [3]. One may think, therefore, that any more attempt to argue for or against any of these distributions is like chewing old bones.…”

“…Several distributions widely used to model publication productivity (including Lotka [l], Yule Ill], and Rao's displaced negative binomial [3]) are not defined at zero productivity. Thus, they are unsuited for estimating the total population.…”

Bradford's distribution: From the classical bibliometric ?law? to the more general stochastic models

“…Rao (1980), by examining the distribution is that it cannot fit real data, or as stressed by tribution of scientific productivity, showed that the nega- Sichel (1992), ''the Waring and Yule distributions have tive binomial provided a remarkably better fit than the linear tails in a double logarithmic grid, and hence they Price model. However, when applied to the journal proare unsuitable for representing the upper tails of most ductivity in economics (Rao, 1990), a poor fit has been observed bibliometric size-frequency data,'' (p. 7) since observed.…”

Yes, the GIGP really does work—and is workable!

“…[The earliest example of a negative binomial distribution (NBD) being fitted to what would now be called scientometric data seems to be Neelameghan et al (1969), who termed it a modified Poisson distribution.] The reasonable success of the NBD was extensively reported by Ravichandra Rao (1980Rao ( , 1982, although alternatives were suggested, for example, by Hindle and Worthington (1980). The shortcomings of the NBD are particularly revealed by its failure to describe many of the classic examples of informetric data sets which have notoriously long tails.…”