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.
The probability mass function is given, as a function of the rank n, by
where b and c are parameters of the distribution.
- 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
- Xie, S.; Yang, Y. G.; Bao, Z. Y.; Ke, X. Z.; Liu, X. L. (2009). "Mineral resource analysis by parabolic fractals". Mining Science and Technology (China) 19: 91–19. doi:10.1016/S1674-5264(09)60017-X.
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