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)