trEndpointMLE: Estimator of endpoint

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

Estimator of endpoint

Description

Estimator of endpoint using truncated ML estimates.

Usage

trEndpointMLE(data, gamma, tau, plot = FALSE, add = FALSE, 
              main = "Estimates of endpoint", ...)

Arguments

data	Vector of n observations.
gamma	Vector of n-1 estimates for the EVI obtained from trMLE.
tau	Vector of n-1 estimates for the \tau obtained from trMLE.
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.

Details

The endpoint is estimated as

\hat{T}_{k} = X_{n-k,n} + 1/\hat{\tau}_k[( (1-1/k)/((1+ \hat{\tau}_k (X_{n,n}-X_{n-k,n}))^{-1/\hat{\xi}_k}-1/k))^{\hat{\xi}_k} -1]

with \hat{\gamma}_k and \hat{\tau}_k the truncated ML estimates for \gamma and \tau.

See Beirlant et al. (2017) for more details.

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.

Author(s)

Tom Reynkens.

References

Beirlant, J., Fraga Alves, M. I. and Reynkens, T. (2017). "Fitting Tails Affected by Truncation". Electronic Journal of Statistics, 11(1), 2026–2065.

See Also

trMLE, trDTMLE, trProbMLE, trQuantMLE, trTestMLE, trEndpoint

Examples

# Sample from GPD truncated at 99% quantile
gamma <- 0.5
sigma <- 1.5
X <- rtgpd(n=250, gamma=gamma, sigma=sigma, endpoint=qgpd(0.99, gamma=gamma, sigma=sigma))

# Truncated ML estimator
trmle <- trMLE(X, plot=TRUE, ylim=c(0,2))

# Endpoint
trEndpointMLE(X, gamma=trmle$gamma, tau=trmle$tau, plot=TRUE, ylim=c(0,50))
abline(h=qgpd(0.99, gamma=gamma, sigma=sigma), lty=2)

ReIns documentation built on Nov. 3, 2023, 5:08 p.m.