(Formerly kijfun) Computes a set of K- and K12-functions for all possible pairs of marks \((p,q)\) in a multivariate spatial
point pattern defined in a simple (rectangular or circular)
or complex sampling window (see Details).
kpqfun(p, upto, by)A list of class "fads" with essentially the following components:
a vector of regularly spaced distances (seq(by,upto,by)).
a vector containing the \((p,q)\) paired levels of p$marks.
a data frame containing values of the pair density functions \(g(r)\) and \(g12(r)\).
a data frame containing values of the local neighbour density functions \(n(r)\) and \(n12(r)\).
a data frame containing values of the \(K(r)\) and \(K12(r)\) functions.
a data frame containing values of the modified \(L(r)\) and \(L12(r)\) functions.
Each component except r is a data frame with the following variables:
a vector of estimated values for the observed point pattern.
a vector of theoretical values expected under the null hypotheses of spatial randomness (see kfun) and
population independence (see k12fun).
a "spp" object defining a multivariate spatial point pattern in a given sampling window (see spp).
maximum radius of the sample circles (see Details).
interval length between successive sample circles radii (see Details).
Function kpqfun is simply a wrapper to kfun and k12fun, which computes either K(r)
for points of mark \(p\) when \(p=q\) or K12(r) between the marks \(p\) and \(q\) otherwise.
plot.fads,
spp,
kfun,
k12fun,
kp.fun.