Bradford distribution

Format: Bradford(q, min, max

The Bradford distribution (also known as the 'Bradford Law of Scattering') is similar to a Pareto distribution that has been truncated on the right. It is right-skewed, peaking at its minimum. The greater the value of theta, the faster its density decreases as one moves away from the minimum. It's genesis is essentially empirical, and very similar to the idea behind the Pareto too. Samuel Clement Bradford originally developed data by studying the distribution of articles in journals in two scientific areas, applied geophysics and lubrication. He studied the rates at which articles relevant to each subject area appeared in journals in those areas. He identified all journals that published more than a certain number of articles in the test areas per year, as well as in other ranges of descending frequency. He wrote:

If scientific journals are arranged in order of decreasing productivity of articles on a given subject, they may be divided into a nucleus of periodicals more particularly devoted to the subject and several groups or zones containing the same number of articles as the nucleus, when the numbers of periodicals in the nucleus and succeeding zones will be as 1:n:n2... (Bradford, 1948, p. 116)

Bradford only identified three zones. He found that the value of "n" was roughly 5. So, for example, if a study on a topic finds that six journals contain one-third of the relevant articles found then 6 X 5 = 30 journals will, among them, contain another third of all the relevant articles found, and the last third will be the most scattered of all, being spread out over 6 X 52 = 300 journals.

Bradford's observations are pretty robust. The theory has a lot of implications in researching and investment in periodicals: for example, how many journals an institute should subscribe to, or one should review in a study. It also gives a guide for advertising, by identifying the first third of journals that have the highest impact, helps determine whether journals on a new(ish) topic (or arena like e-journals) have reached a stabilised population, and test the efficiency of Web browsers.


As q approaches zero, Bradford(q,min,max) approaches a Uniform(min,max) distribution.

ModelRisk functions added to Microsoft Excel for the Bradford distribution

VoseBradford generates random values from this distribution for Monte Carlo simulation, or calculates a percentile if used with a U parameter.

VoseBradfordObject constructs a distribution object for this distribution.

VoseBradfordProb returns the probability density or cumulative distribution function for this distribution.

VoseBradfordProb10 returns the log10 of the probability density or cumulative distribution function.  

VoseBradfordFit generates values from this distribution fitted to data, or calculates a percentile from the fitted distribution.

VoseBradfordFitObject constructs a distribution object of this distribution fitted to data.

VoseBradfordFitP returns the parameters of this distribution fitted to data.

Bradford distribution equations



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