Parametric spectral density functions¶
Let
be a multivariate
stationary normal process of dimension
. We only treat here
the case where the domain is of dimension 1:
(
).
If the process is continuous, then
. In the discrete
case,
is a lattice.
This use case illustrates how the User can create a density spectral
function from parametric models. The library proposes the Cauchy
spectral model as a parametric model for the spectral density
function
.
The Cauchy spectral model
Its is associated to the Exponential covariance model. The Cauchy spectral model is defined by:
(1)¶
where ,
and
are the parameters of the Exponential covariance model defined in
section [ParamStationaryCovarianceFunction]. The relation
(1) can be explained with the spatial covariance function
defined in (6).
API:
See
CauchyModel
Examples: