page_title: King effect
hierarchical_section_title: King effect
caption_attribution_description: English: A rank-ordering of the 237 countries listed here. Rescaling the 2011 population allows most countries to be fit by a stretched exponential distribution (estimated by eye here), which shows as a straight line on the semi-log plot shown here. Note that China and India do not fit on this line due to the King effect.
context_page_description: 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, that of a stretched exponential, or a parabolic fractal.
  The King effect has been observed in the distribution of:
  French city sizes, and similarly for other countries with a primate city, such as the United Kingdom, and the extreme case of Bangkok.
  country populations.
  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.
context_section_description: 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, that of a stretched exponential, 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), 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 actually may exist a Pauper effect, with a similar detachment of extremely ranked data points from the reasonably distributed portion of the data set.
caption: Rank-ordering of the population of countries follows a stretched exponential distribution[1] except in the cases of the two "Kings": China and India.
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