ReIns (version 1.0.10)

Hill.2oQV: 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", ...)

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 \(k\).

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.

Author

Tom Reynkens based on S-Plus code from Yuri Goegebeur and R code from Klaus Herrmann.

Details

See Section 4.2.1 of Albrecher et al. (2017) for more details.

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)