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spatstat.core (version 2.3-0)

PPversion: 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.

Value

Another object of class "fv".

Details

The argument f should be an object of class "fv", containing both empirical estimates f^(r) and a theoretical value f0(r) for a summary function.

The P--P version of f is the function g(x)=f^(f01(x)) where f01 is the inverse function of f0. A plot of g(x) against x is equivalent to a plot of f^(r) against f0(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)=f01(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).

See Also

plot.fv

Examples

Run this code
# NOT RUN {
  opa <- par(mar=0.1+c(5,5,4,2))
  G <- Gest(redwoodfull)
  plot(PPversion(G))
  plot(QQversion(G))
  par(opa)
# }

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