evt0 (version 1.1.5)

mop.q: High qunatile estimate by mean of order p statistic

Description

This function compute estimate of high quantile or value-at-risk (VAR) using mean of order p (MOP) method.

Usage

mop.q(x, k, p, q, method = c("MOP", "RBMOP"))

Value

a matrix of EVI and VaR estimates, corresponds to k row and p columns. 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.

p

a vector of mean order.

q

quantile level.

method

Method used, ("MOP", default) and reduced-bias MOP ("RBMOP").

Author

B G Manjunath

Details

For heavy tails, Gomes et al. (2013) introduces a new class of high quantile estimators based on a class of mean of order p (MOP) extreme value index (EVI) estimators is givin by $$Q(k) = (X_{n-k:n}) (k/nq)^{H_p(k)},$$ where \(H_p(k)\) is MOP EVI estimator and \(X_{i:n}\) is order statistic.

References

Brilhante, M.F., Gomes, M.I. and Pestana, D. (2013). A simple generalisation of the Hill estimator. Computational Statistics and Data Analysis, 57, 518-- 535.

Beran, J., Schell, D. and Stehlik, M. (2013). The harmonic moment tail index estimator: asymptotic distribution and robustness. Ann Inst Stat Math, Published Online.

Gomes, M.I., Brilhante, M.F. and Pestana, D. (2013). New reduced-bias estimators of a positive extreme value index. Submitted article.

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

See Also

mop

Examples

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

# estimate EVI and high quantile at level q
mop.q(x,c(1,500,5000,49999), c(-1,0,1),0.5,"RBMOP")