# Generating function for Generalized Pareto families

### Description

Generates an object of class `"GParetoFamily"`

which
represents a Generalized Pareto family.

### Usage

1 2 3 4 |

### Arguments

`loc` |
real: known/fixed threshold/location parameter |

`scale` |
positive real: scale parameter |

`shape` |
positive real: shape parameter |

`of.interest` |
character: which parameters, transformations are of interest. |

`p` |
real or NULL: probability needed for quantile and expected shortfall |

`N` |
real or NULL: expected frequency for expected loss |

`trafo` |
matrix or NULL: transformation of the parameter |

`start0Est` |
startEstimator — if |

`withPos` |
logical of length 1: Is shape restricted to positive values? |

`secLevel` |
a numeric of length 1:
In the ideal GEV model, for each observastion |

`withCentL2` |
logical: shall L2 derivative be centered by substracting
the E()? Defaults to |

`withL2derivDistr` |
logical: shall the distribution of the L2 derivative
be computed? Defaults to |

`..ignoreTrafo` |
logical: only used internally in |

### Details

The slots of the corresponding L2 differentiable parameteric family are filled.

### Value

Object of class `"GParetoFamily"`

### Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

Nataliya Horbenko nataliya.horbenko@itwm.fraunhofer.de

### References

Kohl, M. (2005) *Numerical Contributions to
the Asymptotic Theory of Robustness*. Bayreuth: Dissertation.

M.~Kohl, P. Ruckdeschel, H.~Rieder (2010):
Infinitesimally Robust Estimation in General Smoothly Parametrized Models.
*Stat. Methods Appl.*, **19**, 333–354.

Ruckdeschel, P. and Horbenko, N. (2011): Optimally-Robust Estimators in Generalized
Pareto Models. ArXiv 1005.1476. To appear at *Statistics*.
DOI: 10.1080/02331888.2011.628022.

Ruckdeschel, P. and Horbenko, N. (2012): Yet another breakdown point notion:
EFSBP –illustrated at scale-shape models. *Metrika*, **75**(8),
1025–1047.

### See Also

`L2ParamFamily-class`

, `GPareto`

### Examples

1 2 3 | ```
(G1 <- GParetoFamily())
FisherInfo(G1)
checkL2deriv(G1)
``` |