cEPD: EPD estimator for right censored data

In TReynkens/ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

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", ...)

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.

Details

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

This estimator is only suitable for right censored data.

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.

Author(s)

Tom Reynkens based on R code from Anastasios Bardoutsos.

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)

TReynkens/ReIns documentation built on Nov. 9, 2023, 1:29 p.m.