pcf | R Documentation |

Estimate the pair correlation function.

pcf(X, ...)

`X` |
Either the observed data point pattern,
or an estimate of its |

`...` |
Other arguments passed to the appropriate method. |

The pair correlation function of a stationary point process is

*
g(r) = K'(r)/ ( 2 * pi * r)
*

where *K'(r)* is the derivative of *K(r)*, the
reduced second moment function (aka “Ripley's *K* function”)
of the point process. See `Kest`

for information
about *K(r)*. For a stationary Poisson process, the
pair correlation function is identically equal to 1. Values
*g(r) < 1* suggest inhibition between points;
values greater than 1 suggest clustering.

We also apply the same definition to
other variants of the classical *K* function,
such as the multitype *K* functions
(see `Kcross`

, `Kdot`

) and the
inhomogeneous *K* function (see `Kinhom`

).
For all these variants, the benchmark value of
*K(r) = pi * r^2* corresponds to
*g(r) = 1*.

This routine computes an estimate of *g(r)*
either directly from a point pattern,
or indirectly from an estimate of *K(r)* or one of its variants.

This function is generic, with methods for
the classes `"ppp"`

, `"fv"`

and `"fasp"`

.

If `X`

is a point pattern (object of class `"ppp"`

)
then the pair correlation function is estimated using
a traditional kernel smoothing method (Stoyan and Stoyan, 1994).
See `pcf.ppp`

for details.

If `X`

is a function value table (object of class `"fv"`

),
then it is assumed to contain estimates of the *K* function
or one of its variants (typically obtained from `Kest`

or
`Kinhom`

).
This routine computes an estimate of *g(r)*
using smoothing splines to approximate the derivative.
See `pcf.fv`

for details.

If `X`

is a function value array (object of class `"fasp"`

),
then it is assumed to contain estimates of several *K* functions
(typically obtained from `Kmulti`

or
`alltypes`

). This routine computes
an estimate of *g(r)* for each cell in the array,
using smoothing splines to approximate the derivatives.
See `pcf.fasp`

for details.

Either a function value table
(object of class `"fv"`

, see `fv.object`

)
representing a pair correlation function,
or a function array (object of class `"fasp"`

,
see `fasp.object`

)
representing an array of pair correlation functions.

Stoyan, D. and Stoyan, H. (1994) Fractals, random shapes and point fields: methods of geometrical statistics. John Wiley and Sons.

`pcf.ppp`

,
`pcf.fv`

,
`pcf.fasp`

,
`Kest`

,
`Kinhom`

,
`Kcross`

,
`Kdot`

,
`Kmulti`

,
`alltypes`

# ppp object X <- simdat p <- pcf(X) plot(p) # fv object K <- Kest(X) p2 <- pcf(K, spar=0.8, method="b") plot(p2) # multitype pattern; fasp object amaK <- alltypes(amacrine, "K") amap <- pcf(amaK, spar=1, method="b") plot(amap)

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