# trEndpointMLE: Estimator of endpoint In ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

## Description

Estimator of endpoint using truncated ML estimates.

## Usage

 1 2 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 τ 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

\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.

## Value

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.

## References

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

trMLE, trDTMLE, trProbMLE, trQuantMLE, trTestMLE, trEndpoint

## Examples

  1 2 3 4 5 6 7 8 9 10 11 # 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) 

### Example output




ReIns documentation built on July 2, 2020, 4:03 a.m.