ProbReg {ReIns} | R Documentation |
Estimator of small tail probability in regression
Description
Estimator of small tail probability in the regression case where
is constant and the regression modelling is thus only solely placed on the scale parameter.
Usage
ProbReg(Z, A, q, plot = FALSE, add = FALSE,
main = "Estimates of small exceedance probability", ...)
Arguments
Z |
Vector of |
A |
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 estimator is defined as
with the Hill estimator. Here, it is assumed that we have equidistant covariates
.
See Section 4.4.1 in Albrecher et al. (2017) for more details.
Value
A list with following components:
k |
Vector of the values of the tail parameter |
P |
Vector of the corresponding probability estimates. |
q |
The used large quantile. |
Author(s)
Tom Reynkens.
References
Albrecher, H., Beirlant, J. and Teugels, J. (2017). Reinsurance: Actuarial and Statistical Aspects, Wiley, Chichester.
See Also
Examples
data(norwegianfire)
Z <- norwegianfire$size[norwegianfire$year==76]
i <- 100
n <- length(Z)
# Scale estimator in i/n
A <- ScaleReg(i/n, Z, h=0.5, kernel = "epanechnikov")$A
# Small exceedance probability
q <- 10^6
ProbReg(Z, A, q, plot=TRUE)
# Large quantile
p <- 10^(-5)
QuantReg(Z, A, p, plot=TRUE)