ReIns (version 1.0.10)

trDTMLE: Truncation odds

Description

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

Usage

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

Value

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 \(D_T\).

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.

Author

Tom Reynkens.

Details

The truncation odds is defined as $$D_T=(1-F(T))/F(T)$$ with \(T\) the upper truncation point and \(F\) the CDF of the untruncated distribution (e.g. GPD).

We estimate this truncation odds as $$\hat{D}_T=\max\{ (k+1)/(n+1) ( (1+\hat{\tau}_k E_{1,k})^{-1/\hat{\xi}_k} - 1/(k+1) ) / (1-(1+\hat{\tau}_k E_{1,k})^{-1/\hat{\xi}_k}), 0\}$$ with \(E_{1,k} = X_{n,n}-X_{n-k,n}\).

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

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, trEndpointMLE, trProbMLE, trQuantMLE, trTestMLE, trDT

Examples

Run this code
# 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))

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

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