cHill {ReIns}

Hill estimator for right censored data

Description

Computes the Hill estimator for positive extreme value indices, adapted for right censoring, as a function of the tail parameter k (Beirlant et al., 2007). Optionally, these estimates are plotted as a function of k.

Usage

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

...

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

Details

The Hill estimator adapted for right censored data is equal to the ordinary Hill estimator H_{k,n} divided by the proportion of the k largest observations that is non-censored.

This estimator is only suitable for right censored data, use icHill for interval censored data.

See Section 4.3.2 of Albrecher et al. (2017) for more details.

Value

A list with following components:

k

Vector of the values of the tail parameter k.

gamma1

Vector of the corresponding Hill estimates.

Author(s)

Tom Reynkens

References

Albrecher, H., Beirlant, J. and Teugels, J. (2017). Reinsurance: Actuarial and Statistical Aspects, Wiley, Chichester.

Beirlant, J., Guillou, A., Dierckx, G. and Fils-Villetard, A. (2007). "Estimation of the Extreme Value Index and Extreme Quantiles Under Random Censoring." Extremes, 10, 151–174.

See Also

Hill, icHill, cParetoQQ, cProb, cQuant

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)

# Hill estimator adapted for right censoring
chill <- cHill(Z, censored=censored, plot=TRUE)