ReIns (version 1.0.7)

QuantMOM: Estimator of extreme quantiles using MOM

Description

Compute estimates of an extreme quantile \(Q(1-p)\) using the Method of Moments estimates of the EVI.

Usage

QuantMOM(data, gamma, p, plot = FALSE, add = FALSE, 
         main = "Estimates of extreme quantile", ...)

Arguments

data

Vector of \(n\) observations.

gamma

Vector of \(n-1\) estimates for the EVI obtained from Moment.

p

The exceedance probability of the quantile (we estimate \(Q(1-p)\) for \(p\) small).

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 "Estimates of extreme quantile".

…

Additional arguments for the plot function, see plot for more details.

Value

A list with following components:

k

Vector of the values of the tail parameter \(k\).

Q

Vector of the corresponding quantile estimates.

p

The used exceedance probability.

Details

See Section 4.2.2 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., 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

ProbMOM, Moment, QuantGH, Quant

Examples

# NOT RUN {
data(soa)

# Look at last 500 observations of SOA data
SOAdata <- sort(soa$size)[length(soa$size)-(0:499)]

# MOM estimator
M <- Moment(SOAdata)

# Large quantile
p <- 10^(-5)
QuantMOM(SOAdata, p=p, gamma=M$gamma, plot=TRUE)
# }