GEV | R Documentation |

The functions `GEVfisher()`

and `GEVquasi()`

each define the generalized
extreme value (GEV) family distribution, a three parameter distribution, for
a `gamlss.dist::gamlss.family()`

object to
be used in GAMLSS fitting using the function
`gamlss::gamlss()`

. The only difference
between `GEVfisher()`

and `GEVquasi()`

is the form of scoring method used to
define the weights used in the fitting algorithm. Fisher's scoring,
based on the expected Fisher information is used in `GEVfisher()`

, whereas
a quasi-Newton scoring, based on the cross products of the first derivatives
of the log-likelihood, is used in `GEVquasi()`

. The functions
`dGEV`

, `pGEV`

, `qGEV`

and `rGEV`

define the density, distribution function,
quantile function and random generation for the specific parameterization of
the generalized extreme value distribution given in **Details** below.

```
GEVfisher(mu.link = "identity", sigma.link = "log", nu.link = "identity")
GEVquasi(mu.link = "identity", sigma.link = "log", nu.link = "identity")
dGEV(x, mu = 0, sigma = 1, nu = 0, log = FALSE)
pGEV(q, mu = 0, sigma = 1, nu = 0, lower.tail = TRUE, log.p = FALSE)
qGEV(p, mu = 0, sigma = 1, nu = 0, lower.tail = TRUE, log.p = FALSE)
rGEV(n, mu = 0, sigma = 1, nu = 0)
```

`mu.link` |
Defines the |

`sigma.link` |
Defines the |

`nu.link` |
Defines the |

`x` , `q` |
Vector of quantiles. |

`mu` , `sigma` , `nu` |
Vectors of location, scale and shape parameter values. |

`log` , `log.p` |
Logical. If |

`lower.tail` |
Logical. If |

`p` |
Vector of probabilities. |

`n` |
Number of observations. If |

The distribution function of a GEV distribution with parameters
`loc`

= `\mu`

, `scale`

= `\sigma (> 0)`

and
`shape`

= `\xi`

(`= \nu`

) is

```
F(x) = P(X \leq x) = \exp\left\{ -\left[ 1+\xi\left(\frac{x-\mu}{\sigma}\right)
\right]_+^{-1/\xi} \right\},
```

where `x_+ = \max(x, 0)`

. If `\xi = 0`

the
distribution function is defined as the limit as `\xi`

tends to zero.
The support of the distribution depends on `\xi`

: it is
`x \leq \mu - \sigma / \xi`

for `\xi < 0`

;
`x \geq \mu - \sigma / \xi`

for `\xi > 0`

;
and `x`

is unbounded for `\xi = 0`

.
See
https://en.wikipedia.org/wiki/Generalized_extreme_value_distribution
and/or Chapter 3 of Coles (2001) for further information.

For each observation in the data, the restriction that `\xi > -1/2`

is
imposed, which is necessary for the usual asymptotic likelihood theory to be
applicable.

`GEVfisher()`

and `GEVquasi()`

each return a
`gamlss.dist::gamlss.family()`

object
which can be used to fit a regression model with a GEV response
distribution using the
`gamlss::gamlss()`

function. `dGEV()`

gives the density,
`pGEV()`

gives the distribution function, `qGEV()`

gives the quantile
function, and `rGEV()`

generates random deviates.

See the examples in `fitGEV()`

.

Coles, S. G. (2001) *An Introduction to Statistical
Modeling of Extreme Values*, Springer-Verlag, London.
Chapter 3: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/978-1-4471-3675-0_3")}

`fitGEV`

,
`gamlss.dist::gamlss.family()`

,
`gamlss::gamlss()`

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.