# gev

##### The Generalized Extreme Value Distribution

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

- Keywords
- distribution

##### Usage

```
dgev(x, loc=0, scale=1, shape=0, log = FALSE)
pgev(q, loc=0, scale=1, shape=0, lower.tail = TRUE)
qgev(p, loc=0, scale=1, shape=0, lower.tail = TRUE)
rgev(n, loc=0, scale=1, shape=0)
```

##### Arguments

- x, q
- Vector of quantiles.
- p
- Vector of probabilities.
- n
- Number of observations.
- loc, scale, shape
- Location, scale and shape parameters; the
`shape`

argument cannot be a vector (must have length one). - log
- Logical; if
`TRUE`

, the log density is returned. - lower.tail
- Logical; if
`TRUE`

(default), probabilities are P[X <= x],="" otherwise,="" p[x=""> x]

##### Details

The GEV distribution function with parameters $\code{loc} = a$, $\code{scale} = b$ and $\code{shape} = s$ is $$G(z) = \exp\left[-{1+s(z-a)/b}^{-1/s}\right]$$ for $1+s(z-a)/b > 0$, where $b > 0$. If $s = 0$ the distribution is defined by continuity. If $1+s(z-a)/b \leq 0$, the value $z$ is either greater than the upper end point (if $s < 0$), or less than the lower end point (if $s > 0$). The parametric form of the GEV encompasses that of the Gumbel, Frechet and reversed Weibull distributions, which are obtained for $s = 0$, $s > 0$ and $s < 0$ respectively. It was first introduced by Jenkinson (1955).

##### Value

`dgev`

gives the density function,`pgev`

gives the distribution function,`qgev`

gives the quantile function, and`rgev`

generates random deviates.

##### References

Jenkinson, A. F. (1955)
The frequency distribution of the annual maximum (or minimum) of
meteorological elements.
*Quart. J. R. Met. Soc.*, **81**, 158--171.

##### See Also

##### Examples

```
dgev(2:4, 1, 0.5, 0.8)
pgev(2:4, 1, 0.5, 0.8)
qgev(seq(0.9, 0.6, -0.1), 2, 0.5, 0.8)
rgev(6, 1, 0.5, 0.8)
p <- (1:9)/10
pgev(qgev(p, 1, 2, 0.8), 1, 2, 0.8)
## [1] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
```

*Documentation reproduced from package evd, version 2.1-0, License: GPL (Version 2 or above)*