QuantGPD: Estimator of extreme quantiles using GPD-MLE

In TReynkens/ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

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", ...)

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.

Details

See Section 4.2.2 in Albrecher et al. (2017) 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.

Author(s)

Tom Reynkens.

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

ProbGPD, GPDmle, Quant

Examples

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)

TReynkens/ReIns documentation built on Nov. 9, 2023, 1:29 p.m.