Transform a Function into its P-P or Q-Q 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 P-P plot or Q-Q plot
of the original f.
PPversion(f, theo = "theo", columns = ".") QQversion(f, theo = "theo", columns = ".")
f |
The function to be transformed. An object of class |
theo |
The name of the column of |
columns |
Character vector, specifying the columns of |
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 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).
Another object of class "fv".
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.
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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