R: The Generalized Extreme Value Distribution

Generalized Extreme Value Distribution {SpatialExtremes} | R Documentation

## The Generalized Extreme Value Distribution

### Description

Density, distribution function, quantile function and random generation for the GP distribution with location equal to 'loc', scale equal to 'scale' and shape equal to 'shape'.

### Usage

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

### Arguments

`x, q` | vector of quantiles.
`p` | vector of probabilities.
`n` | number of observations.
`loc` | vector of the location parameters.
`scale` | vector of the scale parameters.
`shape` | a numeric of the shape parameter.
`lower.tail` | logical; if TRUE (default), probabilities are Pr[ X <= x], otherwise, Pr[X > x].
`log` | logical; if TRUE, probabilities p are given as log(p).

### Value

If 'loc', 'scale' and 'shape' are not specified they assume the default values of '0', '1' and '0', respectively.

The GEV distribution function for loc = u, scale = σ and shape = ξ is

G(z) = exp[-{1 + ξ (x - u) / σ}^(-1/ξ)]

for 1 + ξ (x - u) / σ > 0 and x > u, where σ > 0. If ξ = 0, the distribution is defined by continuity corresponding to the Gumbel distribution.

### Examples

    dgev(0.1)
    rgev(100, 1, 2, 0.2)
    qgev(seq(0.1, 0.9, 0.1), 1, 0.5, -0.2)
    pgev(12.6, 2, 0.5, 0.1)

[Package SpatialExtremes version 2.0-5 Index]