The command `localL`

computes the *neighbourhood density function*,
a local version of the \(L\)-function (Besag's transformation of Ripley's
\(K\)-function) that was proposed by Getis and Franklin (1987).
The command `localK`

computes the corresponding
local analogue of the K-function.

Given a spatial point pattern `X`

, the neighbourhood density function
\(L_i(r)\) associated with the \(i\)th point
in `X`

is computed by
$$
L_i(r) = \sqrt{\frac a {(n-1) \pi} \sum_j e_{ij}}
$$
where the sum is over all points \(j \neq i\) that lie
within a distance \(r\) of the \(i\)th point,
\(a\) is the area of the observation window, \(n\) is the number
of points in `X`

, and \(e_{ij}\) is an edge correction
term (as described in `Kest`

).
The value of \(L_i(r)\) can also be interpreted as one
of the summands that contributes to the global estimate of the L
function.

By default, the function \(L_i(r)\) or
\(K_i(r)\) is computed for a range of \(r\) values
for each point \(i\). The results are stored as a function value
table (object of class `"fv"`

) with a column of the table
containing the function estimates for each point of the pattern
`X`

.

Alternatively, if the argument `rvalue`

is given, and it is a
single number, then the function will only be computed for this value
of \(r\), and the results will be returned as a numeric vector,
with one entry of the vector for each point of the pattern `X`

.

Inhomogeneous counterparts of `localK`

and `localL`

are computed by `localKinhom`

and `localLinhom`

.