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

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

1 |

`X` |
The observed point pattern,
from which an estimate of |

`...` |
Other arguments passed to |

This command computes an estimate of the *L*-function
for the spatial point pattern `X`

.
The *L*-function is a transformation of Ripley's *K*-function,

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

where *K(r)* is the *K*-function.

See `Kest`

for information
about Ripley's *K*-function. The transformation to *L* was
proposed by Besag (1977).

The command `Lest`

first calls
`Kest`

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

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

See `Kest`

for the list of arguments.

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.

If the argument `var.approx=TRUE`

is given, the return value
includes columns `rip`

and `ls`

containing approximations
to the variance of *Lest(r)* under CSR.
These are obtained by the delta method from the variance
approximations described in `Kest`

.

and \rolf

Besag, J. (1977)
Discussion of Dr Ripley's paper.
*Journal of the Royal Statistical Society, Series B*,
**39**, 193–195.

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