# guplot: Gumbel Plot In VGAM: Vector Generalized Linear and Additive Models

## Description

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

## Usage

 ```1 2 3 4``` ```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.

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.

`gumbel`, `gumbelff`, `gev`, `venice`.
 ```1 2 3 4 5 6``` ```## Not run: guplot(rnorm(500), las = 1) -> ii names(ii) guplot(with(venice, r1), col = "blue") # Venice sea levels data ## End(Not run) ```