cEPD function

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", ...)

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.

Returns

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.

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.

Author(s)

Tom Reynkens based on R code from Anastasios Bardoutsos.

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)