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 = ".")"fv".
f that should be treated as the
theoretical value of the function.
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.
"fv".
f should be an object of class "fv",
containing both empirical estimates $fhat(r)$
and a theoretical value $f0(r)$ for a summary function. The P--P version of f is the function
$g(x) = fhat(f0^(-1)(x))$
where $f0^(-1)$ is the inverse function of
$f0$.
A plot of $g(x)$ against $x$
is equivalent to a plot of $fhat(r)$ 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
$f0^(-1)(fhat(x))$.
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).
plot.fv
G <- Gest(redwoodfull)
plot(PPversion(G))
plot(QQversion(G))
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