spatstat.model (version 3.3-5)

measureWeighted: Weighted Version of a Measure

Description

Given a measure m (object of class "msr") and a spatially-varying weight function, construct the weighted version of m.

Usage

measureWeighted(m, w)

Value

Another measure (object of class "msr") on the same spatial domain.

Arguments

m

A measure (object of class "msr").

w

A pixel image (object of class "im") or a function(x,y) giving the numeric weight at each spatial location.

Author

Adrian Baddeley .

Details

For any region of space B, the weighted measure wm has the value $$ wm(B) = \int_B w(x) dm(x) $$ In any small region of space, the increment of the weighted measure wm is equal to the increment of the original measure m multiplied by the weight w at that location.

References

Halmos, P.R. (1950) Measure Theory. Van Nostrand.

See Also

msr, with.msr, split.msr, measurePositive

Examples

   fit <- ppm(cells ~ x)
   res <- residuals(fit)
   measureWeighted(res, function(x,y){x})