A characterization of distributions which satisfy Price’s law and consequences for the law of Zipf and Mandelbrot

Abstract

The distributions satisfying Price’s Law are characterized. From this it is seen that the Laws of Zipf and of Mandelbrot can satisfy Price’s Law only approximately. The form that Price’s Law takes for these two distributions is then explicitly calculated. In the case of the Law of Mandelbrot, the same Law of Price is discovered as in "L. Egghe. An exact calculation of Price’s Law for the Law of Lotka" (to appear in Scientometrics). This was expected, since the Laws of Lotka and of Mandelbrot are equivalent. The method used in this paper however is simpler.