Second order tail index estimator of Fraga Alves et al. Estimator of the second order regular variation parameter \(\rho \leq 0\) parameter for heavy-tailed data proposed by Fraga Alves et al. (2003)

Second order tail index estimator of Fraga Alves et al. Estimator of the second order regular variation parameter \(\rho \leq 0\) parameter for heavy-tailed data proposed by Fraga Alves et al. (2003)

Usage

rho.fagh(xdat, k, tau = 0)

Arguments

xdat

vector of positive observations

k

number of highest order statistics to use for estimation

tau

scalar real tuning parameter. Default values is 0, which is typically chosen whenever \(\rho \ge -1\). The choice \(\tau=1\) otherwise.

References

Fraga Alves, M.I., Gomes, M. Ivette, and de Haan, Laurens (2003). A new class of semi-parametric estimators of the second order parameter. Portugaliae Mathematica. Nova Serie 60(2), 193-213. <http://eudml.org/doc/50867>.

Examples

# Example with rho = -0.2
n <- 1000
xdat <- mev::rgp(n = n, shape = 0.2)
kmin <- floor(n^0.995)
kmax <- ceiling(n^0.999)
rho_est <- rho.fagh(
   xdat = xdat,
   k = n - kmin:kmax)
rho_med <- mean(rho_est$rho)