guplot: Gumbel Plot

In VGAM: Vector Generalized Linear and Additive Models

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

y	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.

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 ith 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.

Value

A list is returned invisibly with the following components.

x	The reduced data.
y	The sorted y data.

Note

The Gumbel distribution is a special case of the GEV distribution with shape parameter equal to zero.

Author(s)

T. W. Yee

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

## Not run: guplot(rnorm(500), las = 1) -> ii
names(ii)

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

## End(Not run)

VGAM documentation built on Sept. 19, 2023, 9:06 a.m.