King effect

The king effect is the name given by Jean Laherrère and Didier Sornette to the phenomenon in natural distributions where the top one or two members of a ranked set are clear outliers. These top one or two members are unexpectedly large and do not conform to the statistical distribution or rank-distribution which the remainder of the set follows.

Distributions typically followed include the power-law distribution, that is a basis for the stretched exponential function, and parabolic fractal distribution. Laherrere and Sornette noted the King effect in the distributions 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).
The popularity of musicians, where Cliff Richard and Elvis Presley ("The King") are the outliers not fitting on a stretched exponential where success is determined by the number of weeks spent at the weekly top 75 rankings.

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.

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.^{[citation needed]}

References

1 2 3 4 Laherrère, J.; Sornette, D. (1998). "Stretched exponential distributions in nature and economy: "fat tails" with characteristic scales". The European Physical Journal B. 2 (4): 525–539. arXiv:cond-mat/9801293. Bibcode:1998EPJB....2..525L. doi:10.1007/s100510050276.
↑ Bardi, Uga (2017). The Seneca Effect: Why Growth is Slow But Collapse is Rapid. Springer. p. 45. ISBN 9783319572079. On the other side of the Power law distribution, that of the very large events, there is another effect that was noted for the first time by Laherrere and Sornette and termed "the king effect;" a large deviation from the distribution for some events/sizes that are unexpectedly large.
↑ Laherrère, Jean (4 April 1996). "Distributions de type "fractal parabolique" dans la Nature". Comptes Rendus de l'Académie des Sciences. Série II a: Sciences de la Terre et des Planétes: 535. Care must, however, be used in cases where the largest object is much larger than the next line, giving what is known as a King Effect. Paris, for example, is anomalously large in comparison with the distribution of the other French towns.
↑ Jayadev, Arjun (2008). "A power law tail in India's wealth distribution: Evidence from survey data". Physica A. 387 (1): 270–276. Bibcode:2008PhyA..387..270J. doi:10.1016/j.physa.2007.08.049.
1 2 Davies, J.A. (2002). "The individual success of musicians, like that of physicists, follows a stretched exponential distribution". The European Physical Journal B. 27 (4): 445–447. Bibcode:2002EPJB...27..445D. doi:10.1140/epjb/e2002-00176-y.
↑ "Why Is Elvis Called "the King of Rock 'n' Roll"?". Retrieved 10-26-2026. {{cite web}}: Check date values in: |accessdate= (help)

[laherrere-1] 1 2 3 4 Laherrère, J.; Sornette, D. (1998). "Stretched exponential distributions in nature and economy: "fat tails" with characteristic scales". The European Physical Journal B. 2 (4): 525–539. arXiv:cond-mat/9801293. Bibcode:1998EPJB....2..525L. doi:10.1007/s100510050276.

[2] Bardi, Uga (2017). The Seneca Effect: Why Growth is Slow But Collapse is Rapid. Springer. p. 45. ISBN 9783319572079. On the other side of the Power law distribution, that of the very large events, there is another effect that was noted for the first time by Laherrere and Sornette and termed "the king effect;" a large deviation from the distribution for some events/sizes that are unexpectedly large.

[3] Laherrère, Jean (4 April 1996). "Distributions de type "fractal parabolique" dans la Nature". Comptes Rendus de l'Académie des Sciences. Série II a: Sciences de la Terre et des Planétes: 535. Care must, however, be used in cases where the largest object is much larger than the next line, giving what is known as a King Effect. Paris, for example, is anomalously large in comparison with the distribution of the other French towns.

[jayadev-4] Jayadev, Arjun (2008). "A power law tail in India's wealth distribution: Evidence from survey data". Physica A. 387 (1): 270–276. Bibcode:2008PhyA..387..270J. doi:10.1016/j.physa.2007.08.049.

[davies-5] 1 2 Davies, J.A. (2002). "The individual success of musicians, like that of physicists, follows a stretched exponential distribution". The European Physical Journal B. 27 (4): 445–447. Bibcode:2002EPJB...27..445D. doi:10.1140/epjb/e2002-00176-y.

[6] "Why Is Elvis Called "the King of Rock 'n' Roll"?". Retrieved 10-26-2026. {{cite web}}: Check date values in: |accessdate= (help)

King effect

See also

References