trDTMLE function

Truncation odds

Estimates of truncation odds of the truncated probability mass under the untruncated distribution using truncated MLE.

trDTMLE(data, gamma, tau, plot = FALSE, add = FALSE, main = "Estimates of DT", ...)

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 $D_T$ should be plotted as a function of $k$, default is FALSE.
• add: Logical indicating if the estimates of $D_T$ should be added to an existing plot, default is FALSE.
• main: Title for the plot, default is "Estimates of DT".
• ...: Additional arguments for the plot function, see plot for more details.

Details

The truncation odds is defined as

with $T$ the upper truncation point and $F$ the CDF of the untruncated distribution (e.g. GPD).

We estimate this truncation odds as

with $E_{1,k} = X_{n,n}-X_{n-k,n}$.

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

Returns

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

• DT: Vector of the corresponding estimates for the truncation odds $D_T$.

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, trEndpointMLE, trProbMLE, trQuantMLE, trTestMLE, trDT

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))


dtmle <- trDTMLE(X, gamma=trmle$gamma, tau=trmle$tau, plot=TRUE, ylim=c(0,0.05))