# Generalized Pareto distribution

### Description

[borrowed from evd]:

The (Three-parameter) generalized Pareto distribution with parameter `loc`

*= a*,
`scale`

*= b*, `shape`

*= c* has density:

*f(x) = \frac{1}{b} (1+c z)^(-1/c - 1), \quad z = \frac{x-a}{c}*

for *x > a* (* c ≥q 0*) and *a ≤q x ≤q a - b/c*(*c < 0*).

### Objects from the Class

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

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

.

### Slots

`img`

Object of class

`"Reals"`

.`param`

Object of class

`"GParetoParameter"`

.`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 = "GPareto")`

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

: wrapped access method for slot`shape`

of slot`param`

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

: wrapped access method for slot`loc`

of slot`param`

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

: alias to`loc`

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

: wrapped access method for slot`scale`

of slot`param`

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

: wrapped replace method for slot`shape`

of slot`param`

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

: wrapped replace method for slot`loc`

of slot`param`

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

: alias to`loc<-`

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

: wrapped replace method for slot`scale`

of slot`param`

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

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

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

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

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

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

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

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

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

: exact evaluation using explicit expressions.

### Note

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

### Author(s)

Nataliya Horbenko Nataliya.Horbenko@itwm.fraunhofer.de

### References

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

### See Also

`dgpd`

, `AbscontDistribution-class`

### Examples

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