# distcdf

##### Distribution Function of Interpoint Distance

Computes the cumulative distribution function of the distance between two independent random points in a given window or windows.

##### Usage

`distcdf(W, V=W, ..., dW=1, dV=dW, nr=1024, regularise=TRUE)`

##### Arguments

- W
- A window (object of class
`"owin"`

) containing the first random point. - V
- Optional. Another window containing the second random point.
Defaults to
`W`

. - ...
- Arguments passed to
`as.mask`

to determine the pixel resolution for the calculation. - dV, dW
- Optional. Probability densities (not necessarily normalised)
for the first and second random points respectively.
Data in any format acceptable
to
`as.im`

, for example, a`function(x,y)`

- nr
- Integer. The number of values of interpoint distance $r$ for which the CDF will be computed. Should be a large value!
- regularise
- Logical value indicating whether to smooth the results for very small distances, to avoid discretisation artefacts.

##### Details

This command computes the Cumulative Distribution Function $CDF(r) = Prob(T \le r)$ of the Euclidean distance $T = \|X_1 - X_2\|$ between two independent random points $X_1$ and $X_2$.

In the simplest case, the command `distcdf(W)`

, the random points are
assumed to be uniformly distributed in the same
window `W`

.

Alternatively the two random points may be
uniformly distributed in two different windows `W`

and `V`

.

In the most general case the first point $X_1$ is random
in the window `W`

with a probability density proportional to
`dW`

, and the second point $X_2$ is random in
a different window `V`

with probability density proportional
to `dV`

.

The calculation is performed by numerical integration of the set covariance
function `setcov`

for uniformly distributed points, and
by computing the covariance function `imcov`

in the
general case. The accuracy of the result depends on
the pixel resolution used to represent the windows: this is controlled
by the arguments `...`

which are passed to `as.mask`

.
For example use `eps=0.1`

to specify pixels of size 0.1 units.

The arguments `W`

or `V`

may also be point patterns
(objects of class `"ppp"`

).
The result is the cumulative distribution function
of the distance from a randomly selected point in the point pattern,
to a randomly selected point in the other point pattern or window.

If `regularise=TRUE`

(the default), values of the cumulative
distribution function for very short distances are smoothed to avoid
discretisation artefacts. Smoothing is applied to all distances
shorter than the width of 7 pixels.

##### Value

##### See Also

##### Examples

```
# The unit disc
B <- disc()
plot(distcdf(B))
```

*Documentation reproduced from package spatstat, version 1.42-2, License: GPL (>= 2)*