PORT.q {evt0}

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"))

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").

Details

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

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.

Author(s)

B G Manjunath [e-mail]

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")