PPversion
Transform a Function into its PP or QQ Version
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 PP plot or QQ plot
of the original f
.
 Keywords
 manip, spatial, nonparametric
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 off
, or one of the abbreviations recognised byfvnames
.
Details
The argument 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 PP 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 PP 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 QQ 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 QQ 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 QQ version of Kest(X)
is
essentially equivalent to Lest(X)
.
Value

Another object of class
"fv"
.
See Also
Examples
G < Gest(redwoodfull)
plot(PPversion(G))
plot(QQversion(G))