pgs (version 0.4-0)

dvol.mse: MSE approximation for d-dimensional volume predictors

Description

Compute a MSE approximation for d-dimensional volume predictors. The structure of interest is an isotropic d-dimensional random compact set. The sampling device is a uniform random lattice of figures (point patterns, line segments...). The approximation depends only on sampling parameters and on the mean surface (to be provided) of the structure.

Usage

dvol.mse(x, S = 1, L = 3)

Arguments

x

a lattice of figures, object of class FigLat-class.

S

the mean surface. Default: 1.

L

an integer, the criterion for stopping summation of the Epstein zeta function. Argument of the function Ezeta. Default: 3.

Value

The MSE approximation as a numeric.

See Also

area.mse, vol.mse.

Examples

# Area prediction. Sampling by a lattice of point patterns
area.mse(FigLat(2,RectLat2(),PP2(5,0.1)))

# Volume prediction. Sampling by a unit cubic point lattice
vol.mse(FigLat(3,VecLat(diag(3)),PointPattern(rep(0,3))))