guplot: Gumbel Plot

Description

Produces a Gumbel plot, a diagnostic plot for checking whether the data appears to be from a Gumbel distribution.

Usage

guplot(object, ...)
guplot.default(y, main = "Gumbel Plot", xlab = "Reduced data", ylab = "Observed data", type = "p", ...)
guplot.vlm(object, ...)

Arguments

A numerical vector. NAs etc. are not allowed.

main

Character. Overall title for the plot.

xlab

Character. Title for the x axis.

ylab

Character. Title for the y axis.

type

Type of plot. The default means points are plotted.

object

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.

Value

x: The reduced data.
y: The sorted y data.

Details

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.

References

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.