PPversion: Transform a Function into its P-P or Q-Q Version

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

Transform a Function into its P-P or Q-Q Version

Description

Given a function object f containing both the estimated and theoretical versions of a summary function, these operations combine the estimated and theoretical functions into a new function. When plotted, the new function gives either the P-P plot or Q-Q plot of the original f.

Usage

PPversion(f, theo = "theo", columns = ".")

QQversion(f, theo = "theo", columns = ".")

Arguments

f	The function to be transformed. An object of class "fv".
theo	The name of the column of f that should be treated as the theoretical value of the function.
columns	Character vector, specifying the columns of f to which the transformation will be applied. Either a vector of names of columns of f, or one of the abbreviations recognised by fvnames.

Details

The argument f should be an object of class "fv", containing both empirical estimates \widehat f(r) and a theoretical value f_0(r) for a summary function.

The P–P version of f is the function g(x) = \widehat f (f_0^{-1}(x)) where f_0^{-1} is the inverse function of f_0. A plot of g(x) against x is equivalent to a plot of \widehat f(r) against f_0(r) for all r. If f is a cumulative distribution function (such as the result of Fest or Gest) then this is a P–P plot, a plot of the observed versus theoretical probabilities for the distribution. The diagonal line y=x corresponds to perfect agreement between observed and theoretical distribution.

The Q–Q version of f is the function h(x) = f_0^{-1}(\widehat f(x)). If f is a cumulative distribution function, a plot of h(x) against x is a Q–Q plot, a plot of the observed versus theoretical quantiles of the distribution. The diagonal line y=x corresponds to perfect agreement between observed and theoretical distribution. Another straight line corresponds to the situation where the observed variable is a linear transformation of the theoretical variable. For a point pattern X, the Q–Q version of Kest(X) is essentially equivalent to Lest(X).

Value

Another object of class "fv".

Author(s)

Tom Lawrence and Adrian Baddeley.

Implemented by \spatstatAuthors.

See Also

plot.fv

Examples

  opa <- par(mar=0.1+c(5,5,4,2))
  G <- Gest(redwoodfull)
  plot(PPversion(G))
  plot(QQversion(G))
  par(opa)

spatstat.explore documentation built on Aug. 8, 2025, 7:36 p.m.