MeanExcess_TB {ReIns} | R Documentation |
Mean excess function using Turnbull estimator
Description
Computes mean excess values using the Turnbull estimator. These mean excess values can then be plotted as a function of the empirical quantiles (computed using the Turnbull estimator) or as a function of the tail parameter .
Usage
MeanExcess_TB(L, U = L, censored, trunclower = 0, truncupper = Inf,
plot = TRUE, k = FALSE, intervalpkg = TRUE,
main = "Mean excess plot", ...)
Arguments
L |
Vector of length |
U |
Vector of length |
censored |
A logical vector of length |
trunclower |
Lower truncation point, default is 0. |
truncupper |
Upper truncation point, default is |
plot |
Logical indicating if the mean excess values should be plotted in a mean excess plot, default is |
k |
Logical indicating if the mean excess values are plotted as a function of the tail parameter |
intervalpkg |
Logical indicating if the Turnbull estimator is computed using the implementation in the interval package if this package is installed. Default is |
main |
Title for the plot, default is |
... |
Additional arguments for the |
Details
The mean excess values are given by
where is the Turnbull estimator for the CDF.
More specifically, we use the values
for
where
is the empirical quantile function corresponding to the Turnbull estimator.
Right censored data should be entered as L=l
and U=truncupper
, and left censored data should be entered as L=trunclower
and U=u
.
If the interval package is installed and intervalpkg=TRUE
, the icfit
function is used to compute the Turnbull estimator. Otherwise, survfit.formula
from survival is used.
Use MeanExcess
for non-censored data.
See Section 4.3 in Albrecher et al. (2017) for more details.
Value
A list with following components:
k |
Vector of the values of the tail parameter |
X |
Vector of the empirical quantiles, computed using the Turnbull estimator, corresponding to |
e |
Vector of the mean excess values corresponding to the tail parameters in |
Author(s)
Tom Reynkens
References
Albrecher, H., Beirlant, J. and Teugels, J. (2017). Reinsurance: Actuarial and Statistical Aspects, Wiley, Chichester.
See Also
Examples
# Pareto random sample
X <- rpareto(500, shape=2)
# Censoring variable
Y <- rpareto(500, shape=1)
# Observed sample
Z <- pmin(X, Y)
# Censoring indicator
censored <- (X>Y)
# Right boundary
U <- Z
U[censored] <- Inf
# Mean excess plot
MeanExcess_TB(Z, U, censored, k=FALSE)