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.
PPversion(f, theo = "theo", columns = ".")QQversion(f, theo = "theo", columns = ".")
The function to be transformed. An object of class "fv".
The name of the column of f that should be treated as the
theoretical value of the function.
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.
Another object of class "fv".
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).
# 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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