R: Gumbel Plot

guplot {VGAM} | R Documentation

## 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. `NA`s 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)

[Package VGAM version 1.1-3 Index]