GPD-ML estimator for right censored data
Computes ML estimates of fitting GPD to peaks over a threshold adapted for right censoring.
cGPDmle(data, censored, start = c(0.1,1), warnings = FALSE, logk = FALSE,
plot = FALSE, add = FALSE, main = "POT estimates of the EVI", ...)
cPOT(data, censored, start = c(0.1,1), warnings = FALSE, logk = FALSE,
plot = FALSE, add = FALSE, main = "POT estimates of the EVI", ...)data |
Vector of n observations. |
censored |
A logical vector of length n indicating if an observation is censored. |
start |
Vector of length 2 containing the starting values for the optimisation. The first element
is the starting value for the estimator of γ_1 and the second element is the starting value for the estimator of σ_1. Default is |
warnings |
Logical indicating if possible warnings from the optimisation function are shown, default is |
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 GPD-MLE estimator for the EVI adapted for right censored data is equal to the ordinary GPD-MLE estimator for the EVI divided by the proportion of the k largest observations that is non-censored. The estimates for σ are the ordinary GPD-MLE estimates for σ.
This estimator is only suitable for right censored data.
cPOT is the same function but with a different name for compatibility with POT.
A list with following components:
k |
Vector of the values of the tail parameter k. |
gamma1 |
Vector of the corresponding MLE estimates for the γ_1 parameter of the GPD. |
sigma1 |
Vector of the corresponding MLE estimates for the σ_1 parameter of the GPD. |
Tom Reynkens
Einmahl, J.H.J., Fils-Villetard, A. and Guillou, A. (2008). "Statistics of Extremes Under Random Censoring." Bernoulli, 14, 207–227.
# 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) # GPD-ML estimator adapted for right censoring cpot <- cGPDmle(Z, censored=censored, plot=TRUE)
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