king effect

{{Short description|Phenomenon in statistics where highest-ranked data points are outliers}}

File:Rank order countries.png{{cite journal | url=https://doi.org/10.1007%2Fs100510050276 | doi=10.1007/s100510050276 | title=Stretched exponential distributions in nature and economy: "fat tails" with characteristic scales | date=1998 | last1=Laherrère | first1=J. | last2=Sornette | first2=D. | journal=The European Physical Journal B | volume=2 | issue=4 | pages=525–539 | arxiv=cond-mat/9801293 | bibcode=1998EPJB....2..525L }} except in the cases of the two "kings": China and India.]]

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,{{cite journal| doi=10.1016/j.physa.2007.08.049 | volume=387 | title=A power law tail in India's wealth distribution: Evidence from survey data | year=2008 | journal=Physica A | pages=270–276 | last1 = Jayadev | first1 = Arjun| issue=1 | bibcode=2008PhyA..387..270J }} that is a basis for the stretched exponential function,{{cite journal | url=https://doi.org/10.1140/epjb/e2002-00176-y | doi=10.1140/epjb/e2002-00176-y | title=The individual success of musicians, like that of physicists, follows a stretched exponential distribution | date=2002 | last1=Davies | first1=J.A. | journal=The European Physical Journal B | volume=27 | issue=4 | pages=445–447 | bibcode=2002EPJB...27..445D | url-access=subscription }} 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.{{Citation needed|reason=Can't locate "pauper effect" online|date=October 2024}}