Description Usage Arguments Details Value Author(s) References See Also Examples

Calculates an estimate of the inhomogeneous version of
the *L*-function (Besag's transformation of Ripley's *K*-function)
for a spatial point pattern.

1 |

`...` |
Arguments passed to |

This command computes an estimate of the inhomogeneous version of
the *L*-function for a spatial point pattern

The original *L*-function is a transformation
(proposed by Besag) of Ripley's *K*-function,

*L(r) = sqrt(K(r)/pi)*

where *K(r)* is the Ripley *K*-function of a spatially homogeneous
point pattern, estimated by `Kest`

.

The inhomogeneous *L*-function is the corresponding transformation
of the inhomogeneous *K*-function, estimated by `Kinhom`

.
It is appropriate when the point pattern clearly does not have a
homogeneous intensity of points. It was proposed by
Baddeley, Moller and Waagepetersen (2000).

The command `Linhom`

first calls
`Kinhom`

to compute the estimate of the inhomogeneous K-function,
and then applies the square root transformation.

For a Poisson point pattern (homogeneous or inhomogeneous),
the theoretical value of the inhomogeneous *L*-function is *L(r) = r*.
The square root also has the effect of stabilising
the variance of the estimator, so that *L* is more appropriate
for use in simulation envelopes and hypothesis tests.

An object of class `"fv"`

, see `fv.object`

,
which can be plotted directly using `plot.fv`

.

Essentially a data frame containing columns

`r` |
the vector of values of the argument |

`theo` |
the theoretical value |

together with columns named
`"border"`

, `"bord.modif"`

,
`"iso"`

and/or `"trans"`

,
according to the selected edge corrections. These columns contain
estimates of the function *L(r)* obtained by the edge corrections
named.

and \rolf

Baddeley, A., Moller, J. and Waagepetersen, R. (2000)
Non- and semiparametric estimation of interaction in
inhomogeneous point patterns.
*Statistica Neerlandica* **54**, 329–350.

1 2 3 4 | ```
data(japanesepines)
X <- japanesepines
L <- Linhom(X, sigma=0.1)
plot(L, main="Inhomogeneous L function for Japanese Pines")
``` |

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