Moment: Moment estimator

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

Moment estimator

Description

Compute the moment estimates for real extreme value indices as a function of the tail parameter k. Optionally, these estimates are plotted as a function of k.

Usage

Moment(data, logk = FALSE, plot = FALSE, add = FALSE, 
       main = "Moment estimates of the EVI", ...)

Arguments

data	Vector of n observations.
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 should be plotted as a function of k, default is FALSE.
add	Logical indicating if the estimates should be added to an existing plot, default is FALSE.
main	Title for the plot, default is "Moment estimates of the EVI".
...	Additional arguments for the plot function, see plot for more details.

Details

The moment estimator for the EVI is introduced by Dekkers et al. (1989) and is a generalisation of the Hill estimator.

See Section 4.2.2 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 corresponding moment estimates.

Author(s)

Tom Reynkens based on S-Plus code from Yuri Goegebeur.

References

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.

Dekkers, A.L.M, Einmahl, J.H.J. and de Haan, L. (1989). "A Moment Estimator for the Index of an Extreme-value Distribution." Annals of Statistics, 17, 1833–1855.

See Also

Hill, genHill

Examples

data(soa)

# Hill estimator
H <- Hill(soa$size, plot=FALSE)
# Moment estimator
M <- Moment(soa$size)
# Generalised Hill estimator
gH <- genHill(soa$size, gamma=H$gamma)

# Plot estimates
plot(H$k[1:5000], M$gamma[1:5000], xlab="k", ylab=expression(gamma), type="l", ylim=c(0.2,0.5))
lines(H$k[1:5000], gH$gamma[1:5000], lty=2)
legend("topright", c("Moment", "Generalised Hill"), lty=1:2)

TReynkens/ReIns documentation built on Nov. 9, 2023, 1:29 p.m.