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, [2] that is a basis for the stretched exponential function, [1] [3] 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 [1]), 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 [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 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
References
- ^ a b c d "Stretched exponential distributions in nature and economy: "fat tails" with characteristic scales", J. Laherrère and D. Sornette
- ^ Jayadev, Arjun (2008). "A power law tail in India's wealth distribution: Evidence from survey data". Physica A: Statistical Mechanics and Its Applications. 387: 270–276. doi: 10.1016/j.physa.2007.08.049.
- ^ "The individual success of musicians, like that of physicists, follows a stretch exponential", J.A. Davies