# GEVFamilyMuUnknown

##### Generating function for families of Generalized Extreme Value distributions

Generates an object of class `"GEVFamilyMuUnknown"`

which
represents a Generalized EV family with unknown location parameter `mu`

.

- Keywords
- models

##### Usage

```
GEVFamilyMuUnknown(loc = 0, scale = 1, shape = 0.5, of.interest = c("loc",
"scale", "shape"), p = NULL, N = NULL, trafo = NULL,
start0Est = NULL, withPos = TRUE, secLevel = 0.7,
withCentL2 = FALSE, withL2derivDistr = FALSE, withMDE = FALSE,
..ignoreTrafo = FALSE, ..withWarningGEV = TRUE, ..name = "")
```

##### 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. possibilites are: "scale", "shape", "quantile", "expected loss", "expected shortfall"; a maximum number of two of these may be selected

- 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

`NULL`

`PickandsEstimator`

is used- 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 \(X_i\), the expression \(1+\frac{{\rm shape}(X_i-{\rm loc})}{{\rm scale}}\) must be positive, which in principle could be attacked by a single outlier. Hence for sample size \(n\) we allow for \(\varepsilon n\) violations, interpreting the violations as outliers. Here \(\varepsilon = {\tt secLevel}/\sqrt{n}\).

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

`FALSE`

, but higher accuracy can be achieved when set to`TRUE`

.- withL2derivDistr
logical: shall the distribution of the L2 derivative be computed? Defaults to

`FALSE`

(to speed up computations).- withMDE
logical: should Minimum Distance Estimators be used to find a good starting value for the parameter search? Defaults to

`FALSE`

(to speed up computations). We have seen cases though, where the use of the then employed`PickandsEstimator`

was drastically misleading and subsequently led to bad estimates where it is used as starting value; so where feasible it is a good idea to also try argument`withMDE=TRUE`

for control purposes.- ..ignoreTrafo
logical: only used internally in

`kStepEstimator`

; do not change this.- ..withWarningGEV
logical: shall warnings be issued if shape is large?

- ..name
character: optional alternative name for the parametric family; used in generating interpolating grids.

##### Details

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

##### Value

Object of class `"GEVFamilyMuUnknown"`

##### 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. (2012): Yet another breakdown point notion:
EFSBP --illustrated at scale-shape models. *Metrika*, **75**(8),
1025--1047.

##### See Also

`L2ParamFamily-class`

, `'>GPareto`

##### Examples

```
# NOT RUN {
(G1 <- GEVFamilyMuUnknown())
FisherInfo(G1)
checkL2deriv(G1)
# }
```

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