trEndpoint: Estimator of endpoint

Description

Estimator of endpoint using truncated Hill estimates.

Usage

trEndpoint(data, r = 1, gamma, plot = FALSE, add = FALSE,
           main = "Estimates of endpoint", ...)

Value

A list with following components:

k: Vector of the values of the tail parameter $k$.
Tk: Vector of the corresponding estimates for the endpoint $T$.

Arguments

data: Vector of $n$ observations.
r: Trimming parameter, default is 1 (no trimming).
gamma: Vector of $n-1$ estimates for the EVI obtained from trHill.
plot: Logical indicating if the estimates of $T$ should be plotted as a function of $k$, default is FALSE.
add: Logical indicating if the estimates of $T$ should be added to an existing plot, default is FALSE.
main: Title for the plot, default is "Estimates of endpoint".
...: Additional arguments for the plot function, see plot for more details.

Author

Tom Reynkens based on R code of Dries Cornilly.

Details

The endpoint is estimated as $$\hat{T}_{k,n} = \max\{X_{n-k,n} ( ((X_{n-k,n}/X_{n,n})^{1/\hat{\gamma}_k} - 1/(k+1)) / (1-1/(k+1)))^{-\hat{\gamma}_k}, X_{n,n}\}$$ with $\hat{\gamma}_k$ the Hill estimates adapted for truncation.

See Beirlant et al. (2016) or Section 4.2.3 of Albrecher et al. (2017) for more details.

References

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

Beirlant, J., Fraga Alves, M.I. and Gomes, M.I. (2016). "Tail fitting for Truncated and Non-truncated Pareto-type Distributions." Extremes, 19, 429--462.

Examples

Run this code

# Sample from truncated Pareto distribution.
# truncated at 99% quantile
shape <- 2
X <- rtpareto(n=1000, shape=shape, endpoint=qpareto(0.99, shape=shape))

# Truncated Hill estimator
trh <- trHill(X, plot=TRUE, ylim=c(0,2))

# Endpoint
trEndpoint(X, gamma=trh$gamma, plot=TRUE, ylim=c(8,12))
abline(h=qpareto(0.99, shape=shape), lty=2)

Run the code above in your browser using DataCamp Workspace