# GEV-class

##### Generalized EV distribution

[borrowed from evd]:
The GEV distribution function with parameters `loc`

\(= a\),
`scale`

\(= b\), `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 eqns > 0).

- Keywords
- distribution

##### Note

This class is based on the code provided by the package evd by A. G. Stephenson.

##### Objects from the Class

Objects can be created by calls of the form `new("GEV", loc, scale,shape)`

.
More frequently they are created via the generating function
`GEV`

.

##### Slots

`img`

Object of class

`"Reals"`

.`param`

Object of class

`"GEVParameter"`

.`r`

`rgpd`

`d`

`dgpd`

`p`

`pgpd`

, but vectorized and with special treatment of arguments`lower.tail`

and`log.p`

`q`

`qgpd`

, but vectorized and with special treatment of arguments`lower.tail`

and`log.p`

`gaps`

(numeric) matrix or

`NULL`

`.withArith`

logical: used internally to issue warnings as to interpretation of arithmetics

`.withSim`

logical: used internally to issue warnings as to accuracy

`.logExact`

logical: used internally to flag the case where there are explicit formulae for the log version of density, cdf, and quantile function

`.lowerExact`

logical: used internally to flag the case where there are explicit formulae for the lower tail version of cdf and quantile function

##### Extends

Class `"AbscontDistribution"`

, directly.
Class `"UnivariateDistribution"`

, by class `"AbscontDistribution"`

.
Class `"Distribution"`

, by class `"AbscontDistribution"`

.

##### Methods

- initialize
`signature(.Object = "GEV")`

: initialize method.- shape
`signature(object = "GEV")`

: wrapped access method for slot`shape`

of slot`param`

.- loc
`signature(object = "GEV")`

: wrapped access method for slot`loc`

of slot`param`

.- location
`signature(object = "GEV")`

: alias to`loc`

, to support argument naming of package VGAM.- scale
`signature(x = "GEV")`

: wrapped access method for slot`scale`

of slot`param`

.- shape<-
`signature(object = "GEV")`

: wrapped replace method for slot`shape`

of slot`param`

.- loc<-
`signature(object = "GEV")`

: wrapped replace method for slot`loc`

of slot`param`

.- location<-
`signature(object = "GEV")`

: alias to`loc<-`

, to support argument naming of package VGAM.- scale<-
`signature(x = "GEV")`

: wrapped replace method for slot`scale`

of slot`param`

.- +
`signature(e1 = "GEV", e2 = "numeric")`

: exact method for this transformation --- stays within this class.- *
`signature(e1 = "GEV", e2 = "numeric")`

: exact method for this transformation --- stays within this class if`e2>0`

.- E
`signature(object = "GEV", fun = "missing", cond = "missing")`

: exact evaluation using explicit expressions.- var
`signature(signature(x = "GEV")`

: exact evaluation using explicit expressions.- median
`signature(signature(x = "GEV")`

: exact evaluation using explicit expressions.- IQR
`signature(signature(x = "GEV")`

: exact evaluation using explicit expressions.- skewness
`signature(signature(x = "GEV")`

: exact evaluation using explicit expressions.- kurtosis
`signature(signature(x = "GEV")`

: exact evaluation using explicit expressions.- liesInSupport
`signature(object = "GEV", x = "numeric")`

: checks if`x`

lies in the support of the respective distribution.

##### References

Pickands, J. (1975) *Statistical inference using extreme order
statistics. _Annals of Statistics_, *3*, 119-131.*

##### See Also

##### Examples

```
# NOT RUN {
(P1 <- new("GEV", loc = 0, scale = 1,shape = 0))
plot(P1)
shape(P1)
loc(P1)
scale(P1) <- 4
loc(P1) <- 2
shape(P1) <- -1 # may be negative!
plot(P1)
# }
```

*Documentation reproduced from package RobExtremes, version 1.2.0, License: LGPL-3*