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.
Distributions de type “fractal parabolique” dans la Nature (French, with English summary) (http://www.hubbertpeak.com/laherrere/fractal.htm)
Categories: Probability distributions | Statistics
A probability distribution is a special case of the more general notion of a probability measure, which is a function that assigns probabilities satisfying the Kolmogorov axioms to the measurable sets of a measurable space.
The rectangular distribution is a uniform distribution on [-1/2,1/2].
The triangular distribution on [a, b], a special case of which is the distribution of the sum of two uniformly distributed random variables (the convolution of two uniform distributions).
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