pgs (version 0.4-0)

area.mse: MSE approximation for area predictors

Description

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

Usage

area.mse(x, B = 1, L = 3)

Arguments

x

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

B

the mean perimeter. 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.

References

Kieu, K. and Mora, M. (2006). Precision of stereological planar area predictors. J. Microsc., 222(3), 201-211.

See Also

vol.mse, dvol.mse.

Examples

# Sampling by a unit hexagonal point lattice
area.mse(PPHexLat2())
# Sampling by a unit square point lattice
area.mse(PPRectLat2())
# Sampling by a lattice of point patterns
area.mse(PPRectLat2(n=5,hp=0.1))
# Sampling by quadrats (may be slow)
## Not run: area.mse(QRectLat2(hq=0.5,vq=0.7))
# Sampling by a square lattice of segments (may be slow)
## Not run: area.mse(SRectLat2(end=c(0.5,0.1))
# Sampling by an hexagonal lattice of segments (may be slow)
## Not run: area.mse(SHexLat2(end=c(0.2,0.15)))