cProb {ReIns} | R Documentation |
Estimator of small exceedance probabilities and large return periods using censored Hill
Description
Computes estimates of a small exceedance probability or large return period
using the estimates for the EVI obtained from the Hill estimator adapted for right censoring.
Usage
cProb(data, censored, gamma1, q, plot = FALSE, add = FALSE,
main = "Estimates of small exceedance probability", ...)
cReturn(data, censored, gamma1, q, plot = FALSE, add = FALSE,
main = "Estimates of large return period", ...)
Arguments
data |
Vector of |
censored |
A logical vector of length |
gamma1 |
Vector of |
q |
The used large quantile (we estimate |
plot |
Logical indicating if the estimates should be plotted as a function of |
add |
Logical indicating if the estimates should be added to an existing plot, default is |
main |
Title for the plot, default is |
... |
Additional arguments for the |
Details
The probability is estimated as
with the
-th order statistic of the data,
the Hill estimator adapted for right censoring and
the Kaplan-Meier estimator for the CDF evaluated in
.
Value
A list with following components:
k |
Vector of the values of the tail parameter |
P |
Vector of the corresponding probability estimates, only returned for |
R |
Vector of the corresponding estimates for the return period, only returned for |
q |
The used large quantile. |
Author(s)
Tom Reynkens
References
Beirlant, J., Guillou, A., Dierckx, G. and Fils-Villetard, A. (2007). "Estimation of the Extreme Value Index and Extreme Quantiles Under Random Censoring." Extremes, 10, 151–174.
See Also
cHill
, cQuant
, Prob
, KaplanMeier
Examples
# Set seed
set.seed(29072016)
# 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)
# Hill estimator adapted for right censoring
chill <- cHill(Z, censored=censored, plot=TRUE)
# Small exceedance probability
q <- 10
cProb(Z, censored=censored, gamma1=chill$gamma1, q=q, plot=TRUE)
# Return period
cReturn(Z, censored=censored, gamma1=chill$gamma1, q=q, plot=TRUE)