Compute the spatial cumulative distribution function of a spatial covariate, optionally using spatially-varying weights.

`spatialcdf(Z, weights = NULL, normalise = FALSE, ..., W = NULL, Zname = NULL)`

A cumulative distribution function object
belonging to the classes `"spatialcdf"`

,

`"ewcdf"`

, `"ecdf"`

(only if `normalise=TRUE`

)
and `"stepfun"`

.

- Z
Spatial covariate. A pixel image or a

`function(x,y,...)`

- weights
Spatial weighting for different locations. A pixel image, a

`function(x,y,...)`

, a window, a constant value, or a fitted point process model (object of class`"ppm"`

or`"kppm"`

).- normalise
Logical. Whether the weights should be normalised so that they sum to 1.

- ...
Arguments passed to

`as.mask`

to determine the pixel resolution, or extra arguments passed to`Z`

if it is a function.- W
Optional window (object of class

`"owin"`

) defining the spatial domain.- Zname
Optional character string for the name of the covariate

`Z`

used in plots.

Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.

If `weights`

is missing or `NULL`

, it defaults to 1.
The values of the covariate `Z`

are computed on a grid of pixels. The weighted cumulative distribution
function of `Z`

values is computed, taking each value with weight
equal to the pixel area. The resulting function \(F\) is such that
\(F(t)\) is the area of the region of space where
\(Z \le t\).

If `weights`

is a pixel image or a function, then the
values of `weights`

and of the covariate `Z`

are computed on a grid of pixels. The
`weights`

are multiplied by the pixel area.
Then the weighted empirical cumulative distribution function
of `Z`

values
is computed using `ewcdf`

. The resulting function
\(F\) is such that \(F(t)\) is the total weight (or weighted area)
of the region of space where \(Z \le t\).

If `weights`

is a fitted point process model, then it should
be a Poisson process. The fitted intensity of the model,
and the value of the covariate `Z`

, are evaluated at the
quadrature points used to fit the model. The `weights`

are
multiplied by the weights of the quadrature points.
Then the weighted empirical cumulative distribution of `Z`

values
is computed using `ewcdf`

. The resulting function
\(F\) is such that \(F(t)\) is the expected number of points
in the point process that will fall in the region of space
where \(Z \le t\).

If `normalise=TRUE`

, the function is normalised so that its
maximum value equals 1, so that it gives the cumulative
*fraction* of weight or cumulative fraction of points.

The result can be printed, plotted, and used as a function.

`ewcdf`

,
`cdf.test`

```
with(bei.extra, {
plot(spatialcdf(grad))
if(require("spatstat.model")) {
fit <- ppm(bei ~ elev)
plot(spatialcdf(grad, predict(fit)))
plot(A <- spatialcdf(grad, fit))
A(0.1)
}
})
plot(spatialcdf("x", W=letterR))
```

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