# PPversion: Transform a Function into its P-P or Q-Q Version

### Description

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`.

### Usage

 ```1 2 3``` ```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 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)`.

### Value

Another object of class `"fv"`.

### Author(s)

Implemented by \spatstatAuthors.

`plot.fv`

### Examples

 ```1 2 3 4 5``` ``` 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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