Bias-reduced scale estimator using second order Hill estimator
Computes the bias-reduced estimator for the scale parameter using the second-order Hill estimator.
Scale.2o(data, gamma, b, beta, logk = FALSE, plot = FALSE, add = FALSE,
main = "Estimates of scale parameter", ...)data |
Vector of n observations. |
gamma |
Vector of n-1 estimates for the EVI obtained from |
b |
Vector of n-1 estimates for B obtained from |
beta |
Vector of n-1 estimates for β obtained from |
logk |
Logical indicating if the estimates are plotted as a function of \log(k) ( |
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 |
The scale estimates are computed based on the following model for the CDF: 1-F(x) = A x^{-1/γ} ( 1+ bx^{-β}(1+o(1)) ), where A:= C^{1/γ} is the scale parameter.
See Section 4.2.1 of Albrecher et al. (2017) for more details.
A list with following components:
k |
Vector of the values of the tail parameter k. |
A |
Vector of the corresponding scale estimates. |
C |
Vector of the corresponding estimates for C, see details. |
Tom Reynkens
Albrecher, H., Beirlant, J. and Teugels, J. (2017). Reinsurance: Actuarial and Statistical Aspects, Wiley, Chichester.
Beirlant, J., Schoutens, W., De Spiegeleer, J., Reynkens, T. and Herrmann, K. (2016). "Hunting for Black Swans in the European Banking Sector Using Extreme Value Analysis." In: Jan Kallsen and Antonis Papapantoleon (eds.), Advanced Modelling in Mathematical Finance, Springer International Publishing, Switzerland, pp. 147–166.
data(secura)
# Hill estimator
H <- Hill(secura$size)
# Bias-reduced Hill estimator
H2o <- Hill.2oQV(secura$size)
# Scale estimator
S <- Scale(secura$size, gamma=H$gamma, plot=FALSE)
# Bias-reduced scale estimator
S2o <- Scale.2o(secura$size, gamma=H2o$gamma, b=H2o$b,
beta=H2o$beta, plot=FALSE)
# Plot logarithm of scale
plot(S$k,log(S$A), xlab="k", ylab="log(Scale)", type="l")
lines(S2o$k,log(S2o$A), lty=2)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.