Parabolic fractal distribution

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In the parabolic fractal distribution, 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 external link below).

In a number of cases, 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.

External links

Distributions de type "fractal parabolique" dans la Nature (French, with English summary)

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Probability distributions

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Benford · Bernoulli · binomial · categorical · hypergeometric · Rademacher · discrete uniform · Zipf · Zipf-Mandelbrot

[[Template: {{{name}}}\|v]] • [[Template talk: {{{name}}}\|d]] • [{{fullurl:Template: {{{name}}}\|action=edit}} e] Discrete univariate with infinite support
Boltzmann · Conway-Maxwell-Poisson · compound Poisson · discrete phase-type · Gauss-Kuzmin · geometric · logarithmic · negative binomial · parabolic fractal · Poisson · Skellam · Yule-Simon · zeta

[[Template: {{{name}}}\|v]] • [[Template talk: {{{name}}}\|d]] • [{{fullurl:Template: {{{name}}}\|action=edit}} e] Continuous univariate supported on a bounded interval
Beta · Kumaraswamy · raised cosine · triangular · U-quadratic · uniform · Wigner semicircle

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Continuous univariate supported on a semi-infinite interval

Beta prime · Burr · chi-square · Coxian · Erlang · exponential · F · Fermi-Dirac · folded normal · Fréchet · Gamma · generalized extreme value · generalized inverse Gaussian · half-logistic · half-normal · Hotelling's T-square · hyper-exponential · hypoexponential · inverse chi-square (scale inverse chi-square) · inverse Gaussian · inverse gamma · Lévy · log-normal · log-logistic · Maxwell-Boltzmann · Maxwell speed · Nakagami · noncentral chi-square · Pareto · phase-type · Rayleigh · relativistic Breit–Wigner · Rice · Rosin–Rammler · shifted Gompertz · truncated normal · type-2 Gumbel · Weibull · Wilks' lambda

[[Template: {{{name}}}\|v]] • [[Template talk: {{{name}}}\|d]] • [{{fullurl:Template: {{{name}}}\|action=edit}} e] Continuous univariate supported on the whole real line
Cauchy · extreme value · exponential power · Fisher's z · Fisher-Tippett · generalized hyperbolic · hyperbolic secant · Landau · Laplace · Lévy skew alpha-stable · logistic · normal (Gaussian) · normal inverse Gaussian · skew normal · Student's t · type-1 Gumbel · Variance-Gamma · Voigt

[[Template: {{{name}}}\|v]] • [[Template talk: {{{name}}}\|d]] • [{{fullurl:Template: {{{name}}}\|action=edit}} e] Multivariate (joint)
Discrete: Ewens · multinomial · multivariate Polya Continuous: Dirichlet · Generalized Dirichlet · multivariate normal · multivariate Student · normal-scaled inverse gamma · normal-gamma Matrix-valued: inverse-Wishart · matrix normal · Wishart