EPD estimator for right censored data
Computes the EPD estimates adapted for right censored data.
cEPD(data, censored, rho = -1, beta = NULL, logk = FALSE,
plot = FALSE, add = FALSE, main = "EPD estimates of the EVI", ...)data |
Vector of n observations. |
censored |
A logical vector of length n indicating if an observation is censored. |
rho |
A parameter for the ρ-estimator of Fraga Alves et al. (2003)
when strictly positive or choice(s) for ρ if negative. Default is |
beta |
Parameter for EPD (β=-ρ/γ). If |
logk |
Logical indicating if the estimates are plotted as a function of \log(k) ( |
plot |
Logical indicating if the estimates of γ should be plotted as a function of k, default is |
add |
Logical indicating if the estimates of γ should be added to an existing plot, default is |
main |
Title for the plot, default is |
... |
Additional arguments for the |
The function EPD uses τ which is equal to -β.
This estimator is only suitable for right censored data.
A list with following components:
k |
Vector of the values of the tail parameter k. |
gamma1 |
Vector of the corresponding estimates for the γ parameter of the EPD. |
kappa1 |
Vector of the corresponding MLE estimates for the κ parameter of the EPD. |
beta |
Vector of estimates for (or values of) the β parameter of the EPD. |
Delta |
Difference between |
Tom Reynkens based on R code from Anastasios Bardoutsos.
Beirlant, J., Bardoutsos, A., de Wet, T. and Gijbels, I. (2016). "Bias Reduced Tail Estimation for Censored Pareto Type Distributions." Statistics & Probability Letters, 109, 78–88.
Fraga Alves, M.I. , Gomes, M.I. and de Haan, L. (2003). "A New Class of Semi-parametric Estimators of the Second Order Parameter." Portugaliae Mathematica, 60, 193–214.
# 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) # EPD estimator adapted for right censoring cepd <- cEPD(Z, censored=censored, plot=TRUE)
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