Produces a Gumbel plot, a diagnostic plot for checking whether the data appears to be from a Gumbel distribution.
guplot(object, ...)
guplot.default(y, main = "Gumbel Plot",
xlab = "Reduced data", ylab = "Observed data", type = "p", ...)
guplot.vlm(object, ...)
A list is returned invisibly with the following components.
The reduced data.
The sorted y data.
A numerical vector. NA
s etc. are not allowed.
Character. Overall title for the plot.
Character. Title for the x axis.
Character. Title for the y axis.
Type of plot. The default means points are plotted.
An object that inherits class "vlm"
,
usually of class vglm-class
or
vgam-class
.
Graphical argument passed into
plot
. See par
for an exhaustive list. The arguments xlim
and
ylim
are particularly useful.
T. W. Yee
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.
Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values. London: Springer-Verlag.
Gumbel, E. J. (1958). Statistics of Extremes. New York, USA: Columbia University Press.
gumbel
,
gumbelff
,
gev
,
venice
.
if (FALSE) guplot(rnorm(500), las = 1) -> ii
names(ii)
guplot(with(venice, r1), col = "blue") # Venice sea levels data
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