King effect

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]), 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)
• 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.

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. "A power law tail in India's wealth distribution: Evidence from survey data", Arjun Jayadev
3. "The individual success of musicians, like that of physicists, follows a stretch exponential", J.A. Davies