Name
Title | ||
|---|---|---|
Relations between the shape of a size-frequency distribution and the shape of a rank-frequency distribution |
Abstract | ||
|---|---|---|
We study the dependence of the shape of the rank-frequency distribution g on the shape of the size-frequency distribution f and vice versa. We show mathematically that g is convexly decreasing if and only if f is monotonically decreasing and that g has an S-shape (i.e., g is first convexly decreasing and then concavely decreasing) if and only if f is first increasing and then decreasing. To illustrate our mathematical results, we empirically analyze size- and rank-frequency distributions of the number of articles and of the impact factor of journals in various scientific fields. We find that most of the size-frequency distributions that we examine are first increasing and then decreasing. Most of the rank-frequency distributions that we examine have an S-shape. However, the concave part of the S-shape is sometimes very small. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1016/j.ipm.2010.03.009 | Inf. Process. Manage. |
Keywords | Field | DocType |
size-frequency distribution,concave part,shape,mathematical result,rank-frequency distribution g,rank-frequency distribution,impact factor,various scientific field | Statistical physics,Monotonic function,Data mining,If and only if,Statistics,Mathematics | Journal |
Volume | Issue | ISSN |
47 | 2 | Information Processing and Management |
Citations | PageRank | References |
10 | 0.73 | 9 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| L. Egghe | 1 | 750 | 124.98 |
| Ludo Waltman | 2 | 45 | 3.91 |