R: The Generalized Extreme Value Distribution

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))
    pgev(q, location = 0, scale = 1, shape = 0, lower.tail = TRUE, log.p = FALSE)
    qgev(p, location = 0, scale = 1, shape = 0, lower.tail = TRUE, log.p = FALSE)
    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.
`lower.tail, log.p` | Same meaning as in `punif` or `qunif`.
`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.

### Details

See `gev`, the VGAM family function for estimating the 3 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`, `gevff`, `vglm.control`.

### Examples

     loc <- 2; sigma <- 1; xi <- -0.4
    pgev(qgev(seq(0.05, 0.95, by = 0.05), loc, sigma, xi), loc, sigma, xi)
    ## Not run:  x <- seq(loc - 3, loc + 3, by = 0.01)
    plot(x, dgev(x, loc, sigma, xi), type = "l", col = "blue", ylim = c(0,1),
         main = "Blue is density, orange 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 = "orange")
    abline(h = 0, lty = 2, col = "gray50")

    ## End(Not run)

[Package VGAM version 1.0-3 Index]