King effect explained

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,^[1] that is a basis for the stretched exponential function,^[2] 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.

See also

• Zipf's law
• Didier Sornette

Notes and References

1. 10.1016/j.physa.2007.08.049 . 387 . A power law tail in India's wealth distribution: Evidence from survey data . 2008 . Physica A: Statistical Mechanics and Its Applications . 270–276 . Jayadev . Arjun.
2. http://epjb.edpsciences.org/index.php?option=com_article&access=standard&Itemid=129&url=/articles/epjb/abs/2002/12/b01533/b01533.html "The individual success of musicians, like that of physicists, follows a stretch exponential"