Weissman estimator of extreme quantiles
Compute estimates of an extreme quantile Q(1-p) using the approach of Weissman (1978).
Quant(data, gamma, p, plot = FALSE, add = FALSE,
main = "Estimates of extreme quantile", ...)
Weissman.q(data, gamma, p, plot = FALSE, add = FALSE,
main = "Estimates of extreme quantile", ...)data |
Vector of n observations. |
gamma |
Vector of n-1 estimates for the EVI, typically Hill estimates are used. |
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 as a function of k should be added to an existing plot, default is |
main |
Title for the plot, default is |
... |
Additional arguments for the |
See Section 4.2.1 of Albrecher et al. (2017) for more details.
Weissman.q is the same function but with a different name for compatibility with the old S-Plus code.
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 based on S-Plus code from Yuri Goegebeur.
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.
Weissman, I. (1978). "Estimation of Parameters and Large Quantiles Based on the k Largest Observations." Journal of the American Statistical Association, 73, 812–815.
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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.