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 (with the largest example having rank 1).
Another example is estimating total world oil reserves using the largest fields.
The Laherrère/Deheuvels paper shows the example of Paris, when sorting the sizes of towns in France.
Towns in France excluding Paris closely follow a parabolic distribution, well enough that the 56 largest gave a very good estimate of the population of the country.
That specific effect (intentionally created) may apply to corporate sizes, where the largest businesses use their wealth to buy up smaller rivals.
To test for the King Effect, the distribution must be fitted excluding the 'k' top-ranked items, but without assigning new rank numbers to the remaining members of the population.