Citations and the Zipf-Mandelbrot Law

p1, p2, and p3 all being constants. The same inverse power-law statistical distributions were found in embarrassingly different situations (e.g., [6, 7]). In economics, it was discovered by Pareto [8] over 100 years ago and states that incomes of individuals or firms are inversely proportional to their rank. In less formal words [9], “most success seems to migrate to those people or companies who already are very popular.” In demography [2, 10, 11], city sizes (populations) also are power-like functions of their ranks. The same regularity reveals itself in the distributions of areas covered by satellite cities and villages around huge urban centers [12]. Remarkably enough, as is claimed in [13], in countries such as the former USSR and China, where natural demographic processes were significantly distorted, city sizes do not follow Zipf’s law!