Pratt's measure for some bibliometric distributions and its relation with the 80/20 rule
✍ Scribed by Egghe, L.
- Publisher
- John Wiley and Sons
- Year
- 1987
- Tongue
- English
- Weight
- 873 KB
- Volume
- 38
- Category
- Article
- ISSN
- 0002-8231
No coin nor oath required. For personal study only.
✦ Synopsis
Pratt's measure C on the class concentration of distributions is calculated and interpreted for the laws of Zipf, Mandelbrot, and Lotka, and for the geometric distribution. Comparisons between each are made. We show that phenomena agreeing with Zipf's law are more concentrated than phenomena agreeing with Mandelbrot's law. On the other hand, data following Lotka's law are more concentrated than data following Zipf's law. We also find that the geometric distribution is more concentrated than the Lotka distribution only for high values of the maximal production a source can have. An explicit mathematical formula (in case of the law of Lotka) between C and x(e), the fraction of the sources needed to obtain a fraction 8 of the items produced by these sources (see my earlier article on the 80/20 rule), is derived and tested, unifying these two theories on class concentration. So far, C and x(e) appeared separate in the literature. I .
I. Introduction
In this section we shall introduce the main topics and distributions needed later on and give an outline of the article.
As in [l] we shall use the terminology "a collection of sources having a certain number of items." For the meaning of this sentence, the reader may think of one of the following nonexhaustive list of possibilities. (1) Books in a library having a certain number of borrowings (i.e., books which are borrowed a certain number of times; cf. Burrell [2] or Burrell and Cane [3]).
(2) Journals having a certain number of articles on a certain subject (Bradford's terminology).
(3) Authors in a research center having a certain number of publications (Lotka's terminology). (4) Words having a certain number of occurrences in a text (Zipf's terminology).