In statistics,

economics Economics () is the social science that studies the production, distribution, and consumption of goods and services. Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analy ...

, and

econophysics Econophysics is a 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 and nonlinear dynami ...

, 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 varia ...

or rank-distribution which the remainder of the set obeys. Distributions typically followed include the power-law distribution, that is a basis for the

stretched exponential function The stretched exponential function f_\beta (t) = e^ is obtained by inserting a fractional power law into the exponential function. In most applications, it is meaningful only for arguments between 0 and +∞. With , the usual exponential functio ...

,"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 ( ...

. 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 Bangkok, officially known in 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 estimated populatio ...

(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