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)
# }