QuantGPD: Estimator of extreme quantiles using GPD-MLE

Description

Computes estimates of an extreme quantile \(Q(1-p)\) using the GPD fit for the peaks over a threshold.

Usage

QuantGPD(data, gamma, sigma, 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 \(n-1\) estimates for the EVI obtained from GPDmle.
sigma: Vector of \(n-1\) estimates for \(\sigma\) obtained from GPDmle.
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 in 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.

Examples

Run this code

data(soa)

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

# GPD-ML estimator
pot <- GPDmle(SOAdata)

# Large quantile
p <- 10^(-5)
QuantGPD(SOAdata, p=p, gamma=pot$gamma, sigma=pot$sigma, plot=TRUE)

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