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 = ".")

Another object of class `"fv"`

.

- 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`

.

Tom Lawrence and Adrian Baddeley.

Implemented by Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.

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)`

.

`plot.fv`

```
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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