W: Function W as defined in Theorem 5, in the case when nubar :=...

In cmottet/RobustTail: RobustTail

Description

Function W as defined in Theorem 5, in the case when nubar := 1.

Usage

W(x, w, rho, lambda, H)

Arguments

x, w, rho	Real numbers
lambda	A real number equal to the limit of the ratio H(x)/x^2 as x goes to infinity
H	The function H(x) as defined in program (5) and (EC.19)

Examples

###
### Consider the case when :
###    * h(x) := I(x >= c)
###    * a : is the threshold a defined in program (1). We arbitrarily set a to
###          the 70th percentile of a standard exponential
###    * c : is arbitrarily fixed to the 90th percentile of a standard exponential
###
### We compute W(x1) as defined in Equation (8), i.e. in the case when
###    * w := mu
###    * rho := sigma
###
a <- qexp(0.7)
c <- qexp(0.9)
H <- function(x) (x - max(c - a,0))^2/2*(x >= max(c - a,0))

# Assume the true distribution function is a standard exponential
eta <- dexp(a)
nu <- dexp(a)
beta <- 1-pexp(a)

mu <- eta/nu
sigma <- 2*beta/nu

x1 <- seq(0,mu, length = 1000)
Wx1 <- sapply(x1, FUN = W, w = mu, rho = sigma, H = H, lambda = 1/2)
plot(x1,Wx1,type = "l", ylab = "W(x1)")

cmottet/RobustTail documentation built on May 13, 2019, 8:44 p.m.