trQuant {ReIns} | R Documentation |
Estimator of large quantiles using truncated Hill
Description
trQuant
computes estimates of large quantiles of the truncated distribution using the estimates for the EVI obtained from the Hill estimator adapted for upper truncation.
trQuantW
computes estimates of large quantiles of the parent distribution
which is unobserved.
Usage
trQuant(data, r = 1, rough = TRUE, gamma, DT, p, plot = FALSE, add = FALSE,
main = "Estimates of extreme quantile", ...)
trQuantW(data, gamma, DT, p, plot = FALSE, add = FALSE,
main = "Estimates of extreme quantile", ...)
Arguments
data |
Vector of |
r |
Trimming parameter, default is |
rough |
Logical indicating if rough truncation is present, default is |
gamma |
Vector of |
DT |
Vector of |
p |
The exceedance probability of the 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
We observe the truncated r.v. where
is the truncation point and
the untruncated r.v.
Under rough truncation, the quantiles for are estimated using
with the Hill estimates adapted for truncation and
the estimates for the truncation odds.
Under light truncation, the quantiles are estimated using the Weissman estimator with the Hill estimates replaced by the truncated Hill estimates:
To decide between light and rough truncation, one can use the test implemented in trTest
.
The quantiles for are estimated using
See Beirlant et al. (2016) or Section 4.2.3 of Albrecher et al. (2017) for more details.
Value
A list with following components:
k |
Vector of the values of the tail parameter |
Q |
Vector of the corresponding quantile estimates. |
p |
The used exceedance probability. |
Author(s)
Tom Reynkens based on R
code of Dries Cornilly.
References
Albrecher, H., Beirlant, J. and Teugels, J. (2017). Reinsurance: Actuarial and Statistical Aspects, Wiley, Chichester.
Beirlant, J., Fraga Alves, M.I. and Gomes, M.I. (2016). "Tail fitting for Truncated and Non-truncated Pareto-type Distributions." Extremes, 19, 429–462.
See Also
trHill
, trDT
, trProb
, trEndpoint
, trTest
, Quant
, trQuantMLE
Examples
# Sample from truncated Pareto distribution.
# truncated at 99% quantile
shape <- 2
X <- rtpareto(n=1000, shape=shape, endpoint=qpareto(0.99, shape=shape))
# Truncated Hill estimator
trh <- trHill(X, plot=TRUE, ylim=c(0,2))
# Truncation odds
dt <- trDT(X, gamma=trh$gamma, plot=TRUE, ylim=c(0,2))
# Large quantile
p <- 10^(-5)
# Truncated distribution
trQuant(X, gamma=trh$gamma, DT=dt$DT, p=p, plot=TRUE)
# Original distribution
trQuantW(X, gamma=trh$gamma, DT=dt$DT, p=p, plot=TRUE, ylim=c(0,1000))