Hill2oQV: Bias-reduced MLE (Quantile view)

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

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 n observations.
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 \gamma, \mu and \sigma, respectively. Default is c(1,1,1).
warnings	Logical indicating if possible warnings from the optimisation function are shown, default is FALSE.
logk	Logical indicating if the estimates are plotted as a function of \log(k) (logk=TRUE) or as a function of k. Default is FALSE.
plot	Logical indicating if the estimates of \gamma should be plotted as a function of k, default is FALSE.
add	Logical indicating if the estimates of \gamma should be added to an existing plot, default is FALSE.
main	Title for the plot, default is "Estimates of the EVI".
...	Additional arguments for the plot function, see plot for more details.

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 k.
gamma	Vector of the ML estimates for the EVI for each value of k.
b	Vector of the ML estimates for the parameter b in the regression model for each value of k.
beta	Vector of the ML estimates for the parameter \beta in the regression model for each value of k.

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)

ReIns documentation built on Nov. 3, 2023, 5:08 p.m.