cgenHill function

Generalised Hill estimator for right censored data

Computes the generalised Hill estimates adapted for right censored data.

cgenHill(data, censored, logk = FALSE, plot = FALSE, add = FALSE, 
         main = "Generalised Hill estimates of the EVI", ...)

Arguments

• data: Vector of $n$ observations.
• censored: A logical vector of length $n$ indicating if an observation is censored.
• 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 $\gamma_1$ should be plotted as a function of $k$, default is FALSE.
• add: Logical indicating if the estimates of $\gamma_1$ should be added to an existing plot, default is FALSE.
• main: Title for the plot, default is "Generalised Hill estimates of the EVI".
• ...: Additional arguments for the plot function, see plot for more details.

Details

The generalised Hill estimator adapted for right censored data is equal to the ordinary generalised Hill estimator divided by the proportion of the $k$ largest observations that is non-censored.

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 generalised Hill estimates.

References

Einmahl, J.H.J., Fils-Villetard, A. and Guillou, A. (2008). "Statistics of Extremes Under Random Censoring." Bernoulli, 14, 207--227.

Author(s)

Tom Reynkens

See Also

genHill, cHill, cProbGH, cQuantGH

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)

# Generalised Hill estimator adapted for right censoring
cghill <- cgenHill(Z, censored=censored, plot=TRUE)