evt0 (version 1.1.5)

PORT.q: Peaks over random threshold high quantile estimate

Description

This function computes high quantile or value-at-risk (VaR) estimate based on peaks over random threshold (PORT) Hill extreme value index (EVI) estimate.

Usage

PORT.q(x, k, q1, q2, method = c("PMOP", "PRBMOP"))

Value

a k dimensional vector of PORT Hill and high quantile estimates. When Method = "RBMOP" shape and scale second order parameters estimates are also returned.

Arguments

x

Data vector.

k

a vector of number of upper order statistics.

q1

quantile for PORT.

q2

quantile level.

method

Method used, ("PMOP", default) and reduced-bias PMOP ("PRBMOP").

Author

B G Manjunath

Details

The computation of the high quantile estimate is based on the work by Gomes et al. (2006).

References

Araujo Santos, P., Fraga Alves, M.I. and Gomes, M.I. (2006). Peaks over random threshold methodology for tail index and quantile estimation. Revstat, 4(3), 227--247.

Gomes, M.I., Figueiredo, F., Henriques-Rodrigues, L. and Miranda, M.C. (2006). A quasi-PORT methodology for VaR based on second-order reduced-bias estimation.

Weissman, I. (1978). Estimation of parameters and large quantiles based on the k largest observations. J. Amer. Statist. Assoc., 73, 812-- 815.

See Also

PORT.Hill

Examples

# generate random samples               
x = rfrechet(50000, loc = 0, scale = 1,shape = 1/0.5)

# estimate PORT Hill and quantile at level q2
PORT.q(x,c(1,500,5000),0.1,0.5,"PRBMOP")