QuantGH function

Estimator of extreme quantiles using generalised Hill

Compute estimates of an extreme quantile $Q(1-p)$ using generalised Hill estimates of the EVI.

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

Arguments

• data: Vector of $n$ observations.
• gamma: Vector of $n-2$ estimates for the EVI obtained from genHill.
• 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.

Details

See Section 4.2.2 of Albrecher et al. (2017) for more details.

Returns

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.

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.

Beirlant, J., Vynckier, P. and Teugels, J.L. (1996). "Excess Function and Estimation of the Extreme-value Index". Bernoulli, 2, 293--318.

Author(s)

Tom Reynkens.

See Also

ProbGH, genHill, QuantMOM, Quant

Examples

data(soa)

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

# Hill estimator
H <- Hill(SOAdata)
# Generalised Hill estimator
gH <- genHill(SOAdata, H$gamma)

# Large quantile
p <- 10^(-5)
QuantGH(SOAdata, p=p, gamma=gH$gamma, plot=TRUE)