Estimator of endpoint
Estimator of endpoint using truncated ML estimates.
trEndpointMLE(data, gamma, tau, plot = FALSE, add = FALSE,
main = "Estimates of endpoint", ...)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 T should be plotted as a function of k, default is |
add |
Logical indicating if the estimates of T should be added to an existing plot, default is |
main |
Title for the plot, default is |
... |
Additional arguments for the |
The endpoint is estimated as
\hat{T}_{k} = X_{n-k,n} + 1/\hat{τ}_k[( (1-1/k)/((1+ \hat{τ}_k (X_{n,n}-X_{n-k,n}))^{-1/\hat{ξ}_k}-1/k))^{\hat{ξ}_k} -1]
with \hat{γ}_k and \hat{τ}_k the truncated ML estimates for γ and τ.
See Beirlant et al. (2017) for more details.
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. |
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)) # 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)
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