If \(Y\) has a Gumbel distribution then plotting the sorted
values \(y_i\) versus the reduced values \(r_i\) should
appear linear. The reduced values are given by
$$r_i = -\log(-\log(p_i)) $$
where \(p_i\) is the \(i\)th plotting position, taken
here to be \((i-0.5)/n\).
Here, \(n\) is the number of observations.
Curvature upwards/downwards may indicate a Frechet/Weibull
distribution, respectively. Outliers may also be detected
using this plot.
The function guplot
is generic, and
guplot.default
and guplot.vlm
are some
methods functions for Gumbel plots.