King effect

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.

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

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 actually 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

References

1. "Stretched exponential distributions in nature and economy: "fat tails" with characteristic scales", J. Laherrère and D. Sornette
2. 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.
3. "The individual success of musicians, like that of physicists, follows a stretch exponential", J.A. Davies