trEndpointMLE function

Estimator of endpoint

Estimator of endpoint using truncated ML estimates.

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

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

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

Returns

A list with following components: - k: Vector of the values of the tail parameter $k$.

• Tk: Vector of the corresponding estimates for the endpoint $T$.

References

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

Author(s)

Tom Reynkens.

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)