gevUC {VGAM} | R Documentation

## The Generalized Extreme Value Distribution

### Description

Density, distribution function, quantile function and random generation for the generalized extreme value distribution (GEV) with location parameter `location`, scale parameter `scale` and shape parameter `shape`.

### Usage

    dgev(x, location=0, scale=1, shape=0, log=FALSE, tolshape0 =
         sqrt(.Machine$double.eps), oobounds.log = -Inf, giveWarning = FALSE)
    pgev(q, location=0, scale=1, shape=0)
    qgev(p, location=0, scale=1, shape=0)
    rgev(n, location=0, scale=1, shape=0)

### Arguments

`x, q` | vector of quantiles.
`p` | vector of probabilities.
`n` | number of observations. If `length(n) > 1` then the length is taken to be the number required.
`location` | the location parameter mu.
`scale` | the (positive) scale parameter sigma. Must consist of positive values.
`shape` | the shape parameter xi.
`log` | Logical. If `log=TRUE` then the logarithm of the density is returned.
`tolshape0` | Positive numeric. Threshold/tolerance value for resting whether xi is zero. If the absolute value of the estimate of xi is less than this value then it will be assumed zero and a Gumbel distribution will be used.
`oobounds.log, giveWarning` | Numeric and logical. The GEV distribution has support in the region satisfying `1+shape*(x-location)/scale > 0`. Outside that region, the logarithm of the density is assigned `oobounds.log`, which equates to a zero density. It should not be assigned a positive number, and ideally is very negative. Since `egev` uses this function it is necessary to return a finite value outside this region so as to allow for half-stepping. Both arguments are in support of this. This argument and others match those of `egev`.

### Details

See `gev`, the VGAM family function for estimating the two parameters by maximum likelihood estimation, for formulae and other details. Apart from `n`, all the above arguments may be vectors and are recyled to the appropriate length if necessary.

### Value

`dgev` gives the density, `pgev` gives the distribution function, `qgev` gives the quantile function, and `rgev` generates random deviates.

### Note

The default value of xi=0 means the default distribution is the Gumbel.

Currently, these functions have different argument names compared with those in the evd package.

### Author(s)

T. W. Yee

### References

Coles, S. (2001) An Introduction to Statistical Modeling of Extreme Values. London: Springer-Verlag.

### See Also

`gev`, `egev`, `vglm.control`.

### Examples

    ## Not run:
    x = seq(-3, 3, by=0.01)
    loc = 0; sigma = 1; xi = -0.4
    plot(x, dgev(x, loc, sigma, xi), type="l", col="blue", ylim=c(0,1),
         main="Blue is density, red is cumulative distribution function",
         sub="Purple are 5,10,...,95 percentiles", ylab="", las=1)
    abline(h=0, col="blue", lty=2)
    lines(qgev(seq(0.05,0.95,by=0.05), loc, sigma, xi),
          dgev(qgev(seq(0.05,0.95,by=0.05), loc, sigma, xi), loc, sigma, xi),
          col="purple", lty=3, type="h")
    lines(x, pgev(x, loc, sigma, xi), type="l", col="red")
    abline(h=0, lty=2)

    pgev(qgev(seq(0.05,0.95,by=0.05), loc, sigma, xi), loc, sigma, xi)
    ## End(Not run)

[Package VGAM version 0.7-9 Index]