TailQuantile_sum {AoE} | R Documentation |
Computes an estimate of a tail quantile of a weighted sum w_x * X + w_y * Y.
TailQuantile_sum(p, w.x = NULL, w.y = NULL, lambda = NULL, tail.x, tail.y, Phi, lower, upper, plot = TRUE)
p |
Tail probability. |
w.x, w.y |
Weights w_x >= 0 and w_y >= 0 for X and Y, respectively; can be vectors (of the same length). |
lambda |
The weights may also be specified in the form w_x = λ and w_y = 1 - λ. |
tail.x |
An object with class attribute "GPD_par" , i.e. the output of a call to the function GPD_par applied to the X data with a single value for k. |
tail.y |
Similarly for Y. |
Phi |
An object with class attribute "AngularMeasure" , i.e. the output of a call to the function AngularMeasure applied to the data. |
lower |
A priori lower bound for the tail quantiles. |
upper |
A priori upper bound for the tail quantiles. |
plot |
If TRUE (the default), the results will be plotted. |
A search is performed to find the value of s
so that the tail probability estimated by TailProb_sum
is equal to p
.
If plot
is TRUE
, the estimated tail probabilities are plotted as a function of w.x
or lambda
.
The function silently returns the vector of tail quantile estimates.
AngularMeasure
, GPD_par
, TailProb_sum
# determine a level s such that # the probability that # a portfolio of stocks ABN AMRO and ING # has a daily logreturn of less than -s # is equal to 0.001 data(ABN, ING) GPD.x <- GPD_par(-ABN, method = "Moment", k = 100) print(GPD.x) GPD.y <- GPD_par(-ING, method = "Moment", k = 100) print(GPD.y) Phi <- AngularMeasure(data.x = -ABN, data.y = -ING, k = 100) TailQuantile_sum(p = 0.001, lambda = (0:10)/10, lower = 0.05, upper = 0.15, tail.x = GPD.x, tail.y = GPD.y, Phi = Phi)