Hill estimator for right censored data
Computes the Hill estimator for positive extreme value indices, adapted for right censoring, as a function of the tail parameter k (Beirlant et al., 2007). Optionally, these estimates are plotted as a function of k.
cHill(data, censored, logk = FALSE, plot = FALSE, add = FALSE,
main = "Hill estimates of the EVI", ...)data |
Vector of n observations. |
censored |
A logical vector of length n indicating if an observation is censored. |
logk |
Logical indicating if the estimates are plotted as a function of \log(k) ( |
plot |
Logical indicating if the estimates of γ_1 should be plotted as a function of k, default is |
add |
Logical indicating if the estimates of γ_1 should be added to an existing plot, default is |
main |
Title for the plot, default is |
... |
Additional arguments for the |
The Hill estimator adapted for right censored data is equal to the ordinary Hill estimator H_{k,n} divided by the proportion of the k largest observations that is non-censored.
This estimator is only suitable for right censored data, use icHill for interval censored data.
See Section 4.3.2 of Albrecher et al. (2017) for more details.
A list with following components:
k |
Vector of the values of the tail parameter k. |
gamma1 |
Vector of the corresponding Hill estimates. |
Tom Reynkens
Albrecher, H., Beirlant, J. and Teugels, J. (2017). Reinsurance: Actuarial and Statistical Aspects, Wiley, Chichester.
Beirlant, J., Guillou, A., Dierckx, G. and Fils-Villetard, A. (2007). "Estimation of the Extreme Value Index and Extreme Quantiles Under Random Censoring." Extremes, 10, 151–174.
# Set seed set.seed(29072016) # Pareto random sample X <- rpareto(500, shape=2) # Censoring variable Y <- rpareto(500, shape=1) # Observed sample Z <- pmin(X, Y) # Censoring indicator censored <- (X>Y) # Hill estimator adapted for right censoring chill <- cHill(Z, censored=censored, plot=TRUE)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.