# PPversion

0th

Percentile

##### 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.

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 of f, or one of the abbreviations recognised by fvnames.

##### Details

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).

##### Value

Another object of class "fv".

plot.fv

• PPversion
• QQversion
##### Examples
# NOT RUN {
opa <- par(mar=0.1+c(5,5,4,2))
G <- Gest(redwoodfull)
plot(PPversion(G))
plot(QQversion(G))
par(opa)
# }

Documentation reproduced from package spatstat, version 1.59-0, License: GPL (>= 2)

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