TailQuantile_sum {AoE}R Documentation

Tail Quantile Estimation for a Sum of Random Variables

Description

Computes an estimate of a tail quantile of a weighted sum w_x * X + w_y * Y.

Usage

TailQuantile_sum(p, w.x = NULL, w.y = NULL, lambda = NULL, 
        tail.x, tail.y, Phi, lower, upper, plot = TRUE)

Arguments

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.

Details

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.

Value

The function silently returns the vector of tail quantile estimates.

See Also

AngularMeasure, GPD_par, TailProb_sum

Examples

# 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)

[Package AoE version 1.0.1 Index]