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In [[statistics]], the '''rational quadratic [[covariance function]]''' is used in [[spatial statistics]], [[geostatistics]], [[machine learning]], image analysis, and other fields where multivariate statistical analysis is conducted on [[metric space]]s. It is commonly used to define the statistical [[covariance]] between measurements made at two points that are ''d'' units distant from each other. Since the covariance only depends on distances between points, it is [[stationary process|stationary]]. If the distance is [[Euclidean distance]], the '''rational quadratic covariance function''' is also [[isotropic]].
 
The '''rational quadratic covariance''' between two points separated by ''d'' distance units is given by
 
:<math>
C(d) = \Bigg(1+\frac{d^2}{2\alpha k^2}\Bigg)^{-\alpha}
</math>
 
where α and ''k'' are non-negative [[parameter]]s of the covariance.
 
{{statistics-stub}}
 
[[Category:Spatial data analysis]]
[[Category:Geostatistics]]
[[Category:Covariance and correlation]]

Latest revision as of 09:51, 25 October 2014

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