statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

economics Economics () is the social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and intera ...

, and

econophysics Econophysics is a Heterodox economics, heterodox interdisciplinary research field, applying theories and methods originally developed by physicists in order to solve problems in economics, usually those including uncertainty or stochastic processes ...

, the king effect is the phenomenon in which the top one or two members of a ranked set show up as clear

outlier In statistics, an outlier is a data point that differs significantly from other observations. An outlier may be due to a variability in the measurement, an indication of novel data, or it may be the result of experimental error; the latter are ...

s. These top one or two members are unexpectedly large because they do not conform to the statistical

distribution Distribution may refer to: Mathematics *Distribution (mathematics), generalized functions used to formulate solutions of partial differential equations * Probability distribution, the probability of a particular value or value range of a vari ...

or rank-distribution which the remainder of the set obeys. Distributions typically followed include the

power-law distribution In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities: one q ...

, that is a basis for the stretched exponential function,"The individual success of musicians, like that of physicists, follows a stretch exponential"
J.A. Davies and

parabolic fractal distribution In probability and statistics, the parabolic fractal distribution is a type of discrete probability distribution in which the logarithm of the frequency or size of entities in a population is a quadratic polynomial of the logarithm of the rank (wi ...

. 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 A primate city is a city that is the largest in its country, province, Federated state, state, or region, and disproportionately larger than any others in the urban hierarchy. A ''primate city distribution'' is a rank-size distribution that has on ...

, such as the United Kingdom (London), and the extreme case of

Bangkok Bangkok, officially known in Thai language, Thai as Krung Thep Maha Nakhon and colloquially as Krung Thep, is the capital and most populous city of Thailand. The city occupies in the Chao Phraya River delta in central Thailand and has an estima ...

(see

list of cities in Thailand Thailand divides its settlements (''thesaban'') into three categories by size: cities (''thesaban nakhon''), towns (''thesaban mueang'') and townships (or subdistrict municipality) (''thesaban tambon''). There are 32 cities as of January 2015. ...

). * 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.

References

{{reflist Statistical data sets Economics effects

See also

References