cgenHill: Generalised Hill estimator for right censored data

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

Generalised Hill estimator for right censored data

Description

Computes the generalised Hill estimates adapted for right censored data.

Usage

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.

Value

A list with following components:

k	Vector of the values of the tail parameter k.
gamma1	Vector of the corresponding generalised Hill estimates.

Author(s)

Tom Reynkens

References

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

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)

TReynkens/ReIns documentation built on Nov. 30, 2024, 3:47 p.m.