compileCDF: Generic Calculation of Cumulative Distribution Function of...

In spatstat.explore: Exploratory Data Analysis for the 'spatstat' Family

Generic Calculation of Cumulative Distribution Function of Distances

Description

A low-level function which calculates the estimated cumulative distribution function of a distance variable.

Usage

compileCDF(D, B, r, ..., han.denom=NULL, check=TRUE)

Arguments

D	A vector giving the distances from each data point to the target.
B	A vector giving the distances from each data point to the window boundary, or censoring distances.
r	An equally spaced, finely spaced sequence of distance values at which the CDF should be estimated.
...	Ignored.
han.denom	Denominator for the Hanisch-Chiu-Stoyan estimator. A single number, or a numeric vector with the same length as r.
check	Logical value specifying whether to check validity of the data, for example, that the vectors D and B have the same length, and contain non-negative numbers.

Details

This low-level function calculates estimates of the cumulative distribution function

F(r) = P(D \le r)

of a distance variable D, given a vector of observed values of D and other information. Examples of this concept include the empty space distance function computed by Fest and the nearest-neighbour distance distribution function Gest.

This function compileCDF and its siblings compileK and compilepcf are useful for code development and for teaching, because they perform a common task, and do the housekeeping required to make an object of class "fv" that represents the estimated function. However, they are not very efficient.

The argument D should be a numeric vector of shortest distances measured from each ‘query’ point to the ‘target’ set. The argument B should be a numeric vector of shortest distances measured from each ‘query’ point to the boundary of the window of observation. All entries of D and B should be non-negative.

compileCDF calculates estimates of the cumulative distribution function F(r) using the border method (reduced sample estimator), the Kaplan-Meier estimator and, if han.denom is given, the Hanisch-Chiu-Stoyan estimator. See Chapter 8 of Baddeley, Rubak and Turner (2015).

The result is an object of class "fv" representing the estimated function. Additional columns (such as a column giving the theoretical value) must be added by the user, with the aid of bind.fv.

Value

An object of class "fv" representing the estimated function.

Author(s)

\adrian

References

\baddrubaturnbook

See Also

compileK.

bind.fv to add more columns.

Examples

  ## Equivalent to Gest(japanesepines)
  X <- japanesepines
  D <- nndist(X)
  B <- bdist.points(X)
  r <- seq(0, 0.25, by=0.01)
  H <- eroded.areas(Window(X), r)
  G <- compileCDF(D=D, B=B, r=r, han.denom=H)
  G <- rebadge.fv(G, new.fname="G", new.ylab=quote(G(r)))
  plot(G)

spatstat.explore documentation built on Oct. 22, 2024, 9:07 a.m.