ReIns (version 1.0.10)

QuantGH: Estimator of extreme quantiles using generalised Hill

Description

Compute estimates of an extreme quantile \(Q(1-p)\) using generalised Hill estimates of the EVI.

Usage

QuantGH(data, gamma, p, plot = FALSE, add = FALSE, 
        main = "Estimates of extreme quantile", ...)

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.

Arguments

data

Vector of \(n\) observations.

gamma

Vector of \(n-2\) estimates for the EVI obtained from genHill.

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.

Author

Tom Reynkens.

Details

See Section 4.2.2 of Albrecher et al. (2017) for more details.

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.

Beirlant, J., Vynckier, P. and Teugels, J.L. (1996). "Excess Function and Estimation of the Extreme-value Index". Bernoulli, 2, 293--318.

See Also

ProbGH, genHill, QuantMOM, Quant

Examples

data(soa)

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

# Hill estimator
H <- Hill(SOAdata)
# Generalised Hill estimator
gH <- genHill(SOAdata, H$gamma)

# Large quantile
p <- 10^(-5)
QuantGH(SOAdata, p=p, gamma=gH$gamma, plot=TRUE)