Estimator of extreme quantiles using generalised Hill
Compute estimates of an extreme quantile Q(1-p) using generalised Hill estimates of the EVI.
QuantGH(data, gamma, p, plot = FALSE, add = FALSE,
main = "Estimates of extreme quantile", ...)data |
Vector of n observations. |
gamma |
Vector of n-2 estimates for the EVI obtained from |
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 |
add |
Logical indicating if the estimates should be added to an existing plot, default is |
main |
Title for the plot, default is |
... |
Additional arguments for the |
See Section 4.2.2 of Albrecher et al. (2017) for more details.
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. |
Tom Reynkens.
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.
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)
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