# spatialcdf

##### Spatial Cumulative Distribution Function

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

- Keywords
- spatial, nonparametric

##### Usage

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

##### Arguments

- 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.

##### Details

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.

##### Value

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

,`"ewcdf"`

,`"ecdf"`

and`"stepfun"`

.

##### See Also

##### Examples

```
with(bei.extra, {
plot(spatialcdf(grad))
fit <- ppm(bei ~ elev)
plot(spatialcdf(grad, predict(fit)))
plot(A <- spatialcdf(grad, fit))
A(0.1)
})
```

*Documentation reproduced from package spatstat, version 1.44-0, License: GPL (>= 2)*