evt0 (version 1.1.5)

PORT.Hill: Peaks over random threshold Hill estimate

Description

This function performs peaks over random threshold (PORT) Hill methodology for estimating extreme value index (EVI) for heavy tailed models.

Usage

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

Value

a k dimensional vector of PORT Hill 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.

q

quantile for PORT.

method

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

Author

B G Manjunath , Frederico Caeiro

Details

The computation of PORT Hill estimator is based on the work by Araujo Santos et al. (2006). Reduced biased PORT Hill computation is based on quasi-PORT methodology, see Gomes et al.

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.

Examples

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

# estimate PORT Hill 
PORT.Hill(x,c(1,500,5000),0.1,"PRBMOP")