King effect

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Rank-ordering of the population of countries follows a stretched exponential distribution[1] except in the cases of the two "Kings": China and India.

In statistics, economics, and econophysics, the King effect refers to the phenomenon where the top one or two members of a ranked set show up as outliers. These top one or two members are unexpectedly large because they do not conform to the statistical distribution or rank-distribution which the remainder of the set obeys.

Distributions typically followed include the power-law distribution,[2] that of a stretched exponential,[1][3] or a parabolic fractal.

The King effect has been observed in the distribution of :

  • French city sizes (where the point representing Paris is the "King", failing to conform to the stretched exponential[1])
  • popularity of musicians,[3] (where Cliff Richard and Elvis Presley are the outliers not fitting on a stretched exponential)
  • country populations (where only the points representing China and India fail to fit a stretched exponential[1]).

Note, however, that the King effect is not limited to outliers with a positive evaluation attached to their rank: for rankings on an undesirable attribute, there actually may exist a Pauper effect, with a similar detachment of extremely ranked data points from the reasonably distributed portion of the data set.

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