Hill.2oQV {ReIns} | R Documentation |
Bias-reduced MLE (Quantile view)
Description
Computes bias-reduced ML estimates of gamma based on the quantile view.
Usage
Hill.2oQV(data, start = c(1,1,1), warnings = FALSE, logk = FALSE,
plot = FALSE, add = FALSE, main = "Estimates of the EVI", ...)
Arguments
data |
Vector of |
start |
A vector of length 3 containing starting values for the first numerical optimisation (see Details). The elements
are the starting values for the estimators of |
warnings |
Logical indicating if possible warnings from the optimisation function are shown, default is |
logk |
Logical indicating if the estimates are plotted as a function of |
plot |
Logical indicating if the estimates of |
add |
Logical indicating if the estimates of |
main |
Title for the plot, default is |
... |
Additional arguments for the |
Details
See Section 4.2.1 of Albrecher et al. (2017) for more details.
Value
A list with following components:
k |
Vector of the values of the tail parameter |
gamma |
Vector of the ML estimates for the EVI for each value of |
b |
Vector of the ML estimates for the parameter |
beta |
Vector of the ML estimates for the parameter |
Author(s)
Tom Reynkens based on S-Plus
code from Yuri Goegebeur and R
code from Klaus Herrmann.
References
Albrecher, H., Beirlant, J. and Teugels, J. (2017). Reinsurance: Actuarial and Statistical Aspects, Wiley, Chichester.
Beirlant J., Dierckx, G., Goegebeur Y. and Matthys, G. (1999). "Tail Index Estimation and an Exponential Regression Model." Extremes, 2, 177–200.
Beirlant J., Goegebeur Y., Segers, J. and Teugels, J. (2004). Statistics of Extremes: Theory and Applications, Wiley Series in Probability, Wiley, Chichester.
Examples
data(norwegianfire)
# Plot bias-reduced MLE (QV) as a function of k
Hill.2oQV(norwegianfire$size[norwegianfire$year==76],plot=TRUE)