spatstat (version 1.64-1)

# Jdot: Multitype J Function (i-to-any)

## Description

For a multitype point pattern, estimate the multitype $$J$$ function summarising the interpoint dependence between the type $$i$$ points and the points of any type.

## Usage

Jdot(X, i, eps=NULL, r=NULL, breaks=NULL, …, correction=NULL)

## Arguments

X

The observed point pattern, from which an estimate of the multitype $$J$$ function $$J_{i\bullet}(r)$$ will be computed. It must be a multitype point pattern (a marked point pattern whose marks are a factor). See under Details.

i

The type (mark value) of the points in X from which distances are measured. A character string (or something that will be converted to a character string). Defaults to the first level of marks(X).

eps

A positive number. The resolution of the discrete approximation to Euclidean distance (see below). There is a sensible default.

r

numeric vector. The values of the argument $$r$$ at which the function $$J_{i\bullet}(r)$$ should be evaluated. There is a sensible default. First-time users are strongly advised not to specify this argument. See below for important conditions on $$r$$.

breaks

This argument is for internal use only.

Ignored.

correction

Optional. Character string specifying the edge correction(s) to be used. Options are "none", "rs", "km", "Hanisch" and "best". Alternatively correction="all" selects all options.

## Value

An object of class "fv" (see fv.object).

Essentially a data frame containing six numeric columns

J

the recommended estimator of $$J_{i\bullet}(r)$$, currently the Kaplan-Meier estimator.

r

the values of the argument $$r$$ at which the function $$J_{i\bullet}(r)$$ has been estimated

km

the Kaplan-Meier estimator of $$J_{i\bullet}(r)$$

rs

the reduced sample'' or border correction'' estimator of $$J_{i\bullet}(r)$$

han

the Hanisch-style estimator of $$J_{i\bullet}(r)$$

un

the uncorrected'' estimator of $$J_{i\bullet}(r)$$ formed by taking the ratio of uncorrected empirical estimators of $$1 - G_{i\bullet}(r)$$ and $$1 - F_{\bullet}(r)$$, see Gdot and Fest.

theo

the theoretical value of $$J_{i\bullet}(r)$$ for a marked Poisson process, namely 1.

The result also has two attributes "G" and "F" which are respectively the outputs of Gdot and Fest for the point pattern.