ReIns (version 1.0.7)

Quant.2oQV: Second order refined Weissman estimator of extreme quantiles (QV)

Description

Compute second order refined Weissman estimator of extreme quantiles \(Q(1-p)\) using the quantile view.

Usage

Quant.2oQV(data, gamma, b, beta, p, plot = FALSE, add = FALSE, 
           main = "Estimates of extreme quantile", ...)
                
Weissman.q.2oQV(data, gamma, b, beta, p, plot = FALSE, add = FALSE, 
                main = "Estimates of extreme quantile", ...)

Arguments

data

Vector of \(n\) observations.

gamma

Vector of \(n-1\) estimates for the EVI obtained from Hill.2oQV.

b

Vector of \(n-1\) estimates for \(b\) obtained from Hill.2oQV.

beta

Vector of \(n-1\) estimates for \(\beta\) obtained from Hill.2oQV.

p

The exceedance probability of the quantile (we estimate \(Q(1-p)\) for \(p\) small).

plot

Logical indicating if the estimates should be plotted as a function of \(k\), default is FALSE.

add

Logical indicating if the estimates should be added to an existing plot, default is FALSE.

main

Title for the plot, default is "Estimates of extreme quantile".

…

Additional arguments for the plot function, see plot for more details.

Value

A list with following components:

k

Vector of the values of the tail parameter \(k\).

Q

Vector of the corresponding quantile estimates.

p

The used exceedance probability.

Details

See Section 4.2.1 of Albrecher et al. (2017) for more details.

Weissman.q.2oQV is the same function but with a different name for compatibility with the old S-Plus code.

References

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

Beirlant J., Goegebeur Y., Segers, J. and Teugels, J. (2004). Statistics of Extremes: Theory and Applications, Wiley Series in Probability, Wiley, Chichester.

See Also

Quant, Hill.2oQV

Examples

# NOT RUN {
data(soa)

# Look at last 500 observations of SOA data
SOAdata <- sort(soa$size)[length(soa$size)-(0:499)]

# Hill estimator
H <- Hill(SOAdata)
# Bias-reduced estimator (QV)
H_QV <- Hill.2oQV(SOAdata)

# Exceedance probability
p <- 10^(-5)
# Weissman estimator
Quant(SOAdata, gamma=H$gamma, p=p, plot=TRUE)

# Second order Weissman estimator (QV)
Quant.2oQV(SOAdata, gamma=H_QV$gamma, beta=H_QV$beta, b=H_QV$b, p=p,
           add=TRUE, lty=2)
# }