TailProb_sum {AoE}R Documentation

Tail Probability Estimation for a Sum of Random Variables

Description

Computes an estimate of the probability that w_x * X + w_y * Y > s, where s is large.

Usage

TailProb_sum(s, w.x = 1, w.y = 1, 
        tail.x, tail.y, Phi, plot = TRUE)

Arguments

s The level for which the probability of excess is to be estimated.
w.x A positive number; the weight w_x of X.
w.y A positive number; the weight w_y of X.
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.
tail.y Idem, now for the Y data.
Phi An object with class attribute "AngularMeasure", i.e. the output of a call to the function AngularMeasure applied to the data.
plot If TRUE (the default), the results will be plotted.

Details

If tail.x$k and tail.y$k are vectors, the tail probability will be estimated for every possible combination of choices of k for X and Y.

If plot is TRUE, the tail probability estimates are plotted as a surface in function of tail.x$k and tail.y$k.

Value

The function invisibly returns a matrix with at position (i,j) the estimated tail probability when the tails of X and Y are estimated for k equal to tail.x$k[i] and tail.x$k[j].

See Also

AngularMeasure, GPD_par, TailQuantile_sum

Examples

# estimate probability that the daily logreturn
# of a balanced portfolio of stocks ABN AMRO and ING
# is less than -0.10, i.e. a loss on the portfolio
# of more than about 10 percent
data(ABN, ING)
GPD.x <- GPD_par(-ABN, method = "Moment", k = (2:30)*10)
GPD.y <- GPD_par(-ING, method = "Moment", k = (2:30)*10)
Phi <- AngularMeasure(data.x = -ABN, data.y = -ING, k = 100)
TailProb_sum(s = 0.10, w.x = 0.5, w.y = 0.5,
        tail.x = GPD.x, tail.y = GPD.y, Phi = Phi)

[Package AoE version 1.0.1 Index]