Description Usage Arguments Details Value Author(s) See Also Examples

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`

.

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`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 \spatstatAuthors.

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