Covariance

A covariance is a positive-definite function that characterizes the correlation between two random variables. In geostatistics, the covariance is computed between two stationary random variables Z₁($\bf u$) and Z₂($\bf u$ + $\bf h$) (if Z₁$\ne$Z₂ the covariance is actually a called a cross-covariance). Because the variables are stationnary, the covariance actually only depends on vector h.

C :  $$\bf h$$ $$\longmapsto$$ C$$\Big($$Z₁($$\bf u$$), Z₂($$\bf u$$ + $$\bf h$$)$$\Big)$$    independent of $$\bf u$$

Associated Types

• Return Type

  A::return_type

  The type of C($\bf u_{1}^{}$,$\bf u_{2}^{}$) (see definition above).

• Argument Type

  A::argument_type

  The type of location u (see definition above).

Refinement of

Assignable

Notations

A		A type that is a model of Covariance
a		an object of type A
U		A type that is a model of Location
u1,u2		two objects of type U
T		A type that represents a real number (e.g. float, double)

Valid Expressions

• Compute covariance

  a(u1,u2)

  Return type:		T
  Semantics:		returns the covariance C(u1,u2).

Models

• Spherical_covariance
• Exponential_covariance