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", ...)
data |
Vector of n observations. |
gamma |
Vector of n-1 estimates for the EVI obtained from |
tau |
Vector of n-1 estimates for the τ obtained from |
plot |
Logical indicating if the estimates of D_T should be plotted as a function of k, default is |
add |
Logical indicating if the estimates of D_T should be added to an existing plot, default is |
main |
Title for the plot, default is |
... |
Additional arguments for the |
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{τ}_k E_{1,k})^{-1/\hat{ξ}_k} - 1/(k+1) ) / (1-(1+\hat{τ}_k E_{1,k})^{-1/\hat{ξ}_k}), 0\}
with E_{1,k} = X_{n,n}-X_{n-k,n}.
See Beirlant et al. (2017) for more details.
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. |
Tom Reynkens.
Beirlant, J., Fraga Alves, M. I. and Reynkens, T. (2017). "Fitting Tails Affected by Truncation". Electronic Journal of Statistics, 11(1), 2026–2065.
# 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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