# gevUC: The Generalized Extreme Value Distribution In VGAM: Vector Generalized Linear and Additive Models

## 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

 ```1 2 3 4 5``` ```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.

T. W. Yee

## References

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

`gev`, `gevff`, `vglm.control`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ``` 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 10,...,90 percentiles", ylab = "", las = 1) abline(h = 0, col = "blue", lty = 2) lines(qgev(seq(0.1, 0.9, by = 0.1), loc, sigma, xi), dgev(qgev(seq(0.1, 0.9, by = 0.1), 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 = (0:10)/10, lty = 2, col = "gray50") ## End(Not run) ```