VaR of splicing fit
Compute Value-at-Risk (VaR_{1-p}=Q(1-p)) of the fitted spliced distribution.
VaR(p, splicefit)
p |
The exceedance probability (we estimate VaR_{1-p}=Q(1-p)). |
splicefit |
A |
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).
Vector of quantiles VaR_{1-p}=Q(1-p).
Tom Reynkens with R code from Roel Verbelen for the mixed Erlang quantiles.
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
## 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)
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