VGAM (version 1.1-14)

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, ...)

Value

A list is returned invisibly with the following components.

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.

See Also

gumbel, gumbelff, gev, venice.

Examples

if (FALSE) guplot(rnorm(500), las = 1) -> ii
names(ii)

guplot(with(venice, r1), col = "blue")  # Venice sea levels data