ReIns (version 1.0.10)

cEPD: EPD estimator for right censored data

Description

Computes the EPD estimates adapted for right censored data.

Usage

cEPD(data, censored, rho = -1, beta = NULL, logk = FALSE, 
     plot = FALSE, add = FALSE, main = "EPD estimates of the EVI", ...)

Value

A list with following components:

k

Vector of the values of the tail parameter \(k\).

gamma1

Vector of the corresponding estimates for the \(\gamma\) parameter of the EPD.

kappa1

Vector of the corresponding MLE estimates for the \(\kappa\) parameter of the EPD.

beta

Vector of estimates for (or values of) the \(\beta\) parameter of the EPD.

Delta

Difference between gamma1 and the Hill estimator for censored data.

Arguments

data

Vector of \(n\) observations.

censored

A logical vector of length \(n\) indicating if an observation is censored.

rho

A parameter for the \(\rho\)-estimator of Fraga Alves et al. (2003) when strictly positive or choice(s) for \(\rho\) if negative. Default is -1.

beta

Parameter for EPD (\(\beta=-\rho/\gamma\)). If NULL (default), beta is estimated by \(-\rho/H_{k,n}\) with \(H_{k,n}\) the Hill estimator.

logk

Logical indicating if the estimates are plotted as a function of \(\log(k)\) (logk=TRUE) or as a function of \(k\). Default is FALSE.

plot

Logical indicating if the estimates of \(\gamma\) should be plotted as a function of \(k\), default is FALSE.

add

Logical indicating if the estimates of \(\gamma\) should be added to an existing plot, default is FALSE.

main

Title for the plot, default is "EPD estimates of the EVI".

...

Additional arguments for the plot function, see plot for more details.

Author

Tom Reynkens based on R code from Anastasios Bardoutsos.

Details

The function EPD uses \(\tau\) which is equal to \(-\beta\).

This estimator is only suitable for right censored data.

References

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.

See Also

EPD, cProbEPD, cGPDmle

Examples

# 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)