VaR function

VaR of splicing fit

Compute Value-at-Risk ($VaR_{1-p}=Q(1-p)$) of the fitted spliced distribution.

VaR(p, splicefit)

Arguments

• p: The exceedance probability (we estimate $VaR_{1-p}=Q(1-p)$).
• splicefit: A SpliceFit object, e.g. output from SpliceFitPareto, SpliceFiticPareto or SpliceFitGPD.

Details

See Reynkens et al. (2017) and Section 4.6 of Albrecher et al. (2017) for details.

Note that VaR(p, splicefit) corresponds to qSplice(p, splicefit, lower.tail = FALSE).

Returns

Vector of quantiles $VaR_{1-p}=Q(1-p)$.

References

Albrecher, H., Beirlant, J. and Teugels, J. (2017). Reinsurance: Actuarial and Statistical Aspects, Wiley, Chichester.

Reynkens, T., Verbelen, R., Beirlant, J. and Antonio, K. (2017). "Modelling Censored Losses Using Splicing: a Global Fit Strategy With Mixed Erlang and Extreme Value Distributions". Insurance: Mathematics and Economics, 77, 65--77.

Verbelen, R., Gong, L., Antonio, K., Badescu, A. and Lin, S. (2015). "Fitting Mixtures of Erlangs to Censored and Truncated Data Using the EM Algorithm." Astin Bulletin, 45, 729--758

Author(s)

Tom Reynkens with R code from Roel Verbelen for the mixed Erlang quantiles.

See Also

qSplice, CTE, SpliceFit, SpliceFitPareto, SpliceFiticPareto, SpliceFitGPD

Examples

## Not run:

# Pareto random sample
X <- rpareto(1000, shape = 2)

# Splice ME and Pareto
splicefit <- SpliceFitPareto(X, 0.6)


p <- seq(0,1,0.01)

# Plot of quantiles
plot(p, qSplice(p, splicefit), type="l", xlab="p", ylab="Q(p)")

# Plot of VaR
plot(p, VaR(p, splicefit), type="l", xlab="p", ylab=bquote(VaR[1-p]))
## End(Not run)