Parabolic fractal distribution
In probability and statistics, the parabolic fractal distribution is a type of discrete probability distribution in which the logarithm of the frequency or size of entities in a population is a quadratic polynomial of the logarithm of the rank. This can markedly improve the fit over a simple power-law relationship (see references below).
In a number of applications, there is a so-called King effect where the highest-ranked item has a significantly greater frequency or size than the model predicts on the basis of the other items.
Definition
The probability mass function is given, as a function of the rank n, by
where b and c are parameters of the distribution.
See also
References
- Laherrère J, Deheuvels P (1996) "Distributions de type 'fractal parabolique' dans la nature" (French, with English summary: "Parabolic fractal" distributions in nature), (http://www.hubbertpeak.com/laherrere/fractal.htm) Comptes rendus de l'Académie des sciences, Série II a: Sciences de la Terre et des Planétes, 322, (7), 535–541
- Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1016/S1674-5264(09)60017-X, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with
|doi=10.1016/S1674-5264(09)60017-Xinstead.
 | This probability-related article is a stub. You can help Wikipedia by expanding it. |