Risk Measures for Scale-Shape Families

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Description

Functions to compute Value-at-Risk (VaR), Conditional Value-at-Risk (CVaR) and Expected Loss (EL) at data from scale-shape families.

Usage

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getVaR(data, model, level, rob=TRUE)
getCVaR(data, model, level, rob=TRUE)
getEL(data, model, N0, rob=TRUE)
## S3 method for class 'riskMeasure'
print(x, level=NULL, ...)

Arguments

data

data at which to compute the risk measure.

model

an object of class "L2ScaleShapeFamily". The parametric family at which to evaluate the risk measure.

level

real: probability needed for VaR and CVaR.

N0

real: expected frequency for expected loss.

rob

logical; if TRUE (default) the RMXE-parametric estimator is used; otherwise the MLE.

x

an object of (S3-)class "riskmeasure".

...

further arguments for print.

Value

The risk measures getVaR, getCVaR, getEL return an (S3) object of class "riskMeasure", i.e., a numeric vector of length 2 with components "Risk" and "varofRisk" containing the respective risk measure and a corresponding (asymptotic) standard error for the risk measure. To the return class "riskMeasure", there is a particular print-method; if the corresponding argument level is NULL (default) the corresponding standard error is printed together with the risk measure; otherwise a corresponding CLT-based confidence interval for the risk meausre is produced.

Author(s)

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

References

P. Ruckdeschel, N. Horbenko (2013): Optimally-Robust Estimators in Generalized Pareto Models. Statistics 47(4), 762–791. N. Horbenko, P. Ruckdeschel, T. Bae (2011): Robust Estimation of Operational Risk. Journal of Operational Risk 6(2), 3–30.

See Also

GParetoFamily, GEVFamily, WeibullFamily, GammaFamily

Examples

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  set.seed(123)
  GPD <- GParetoFamily(loc=20480, scale=7e4, shape=0.3)
  data <- r(GPD)(500)
  getCVaR(data,GPD,0.99)
  ## Not run:  # to reduce checking time
  getVaR(data,GPD,0.99)
  getEL(data,GPD,5)
  getVaR(data,GPD,0.99, rob=FALSE)
  getEL(data,GPD,5, rob=FALSE)
  getCVaR(data,GPD,0.99, rob=FALSE)
  
## End(Not run)

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