## The Generalized Extreme Value Distribution

### Description

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

### 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
`loc`

= a, `scale`

= b and
`shape`

= s is

*G(x) = exp[-{1+s(z-a)/b}^(-1/s)]*

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 <= 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

`fgev`

, `rfrechet`

,
`rgumbel`

, `rrweibull`

### 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

[Package

*evd* version 2.2-4

Index]