King effect



In statistics, economics, and econophysics, the king effect is the phenomenon in which the top one or two members of a ranked set show up as clear 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, that is a basis for the stretched exponential function, and parabolic fractal distribution. 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 ), and similarly for other countries with a primate city, such as the United Kingdom (London), and the extreme case of Bangkok (see list of cities in Thailand).
 * Country populations (where only the points representing China and India fail to fit a stretched exponential ).

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 may exist a pauper effect, with a similar detachment of extremely ranked data points from the reasonably distributed portion of the data set.