King effect

In <a href="/facts/Statistics/DNPsKGYU">statistics</a>, <a href="/facts/Economics/HYctA2Dn">economics</a>, and <a href="/facts/Econophysics/WxuC9VUu">econophysics</a>, the king effect is the phenomenon in which the top one or two members of a ranked set show up as clear <a href="/facts/Outlier/VBhIzGbx">outliers</a>. These top one or two members are unexpectedly large because they do not conform to the statistical <a href="/facts/Probability_distribution/EpsKKVRu">distribution</a> or <a href="/facts/Rank%25E2%2580%2593size_distribution/1J6G7Wum">rank-distribution</a> which the remainder of the set obeys.
Distributions typically followed include the <a href="/facts/Power_law/DhAjYwwz">power-law distribution</a>, that is a basis for the <a href="/facts/Stretched_exponential_function/czKXrISV">stretched exponential function</a>, and <a href="/facts/Parabolic_fractal_distribution/9uyCV4pp">parabolic fractal distribution</a>.
The King effect has been observed in the distribution of:

<ul><li>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 <a href="/facts/Primate_city/aRpJTCcu">primate city</a>, such as the United Kingdom (London), and the extreme case of <a href="/facts/Bangkok/WRxftcFz">Bangkok</a> (see <a href="/facts/List_of_cities_in_Thailand/y9zdnCSK">list of cities in Thailand</a>).</li>
<li><a href="/facts/List_of_countries_and_dependencies_by_population/N1Fq63C2">Country populations</a> (where only the points representing China and India fail to fit a stretched exponential).</li></ul>
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.

King effect open-in-new

King effect