| expect.Choquet.unif-methods {kappalab} | R Documentation |
Methods for computing the expectation and standard deviation of the Choquet integral in the standard uniform and standard normal cases.
J-L. Marichal and I. Kojadinovic (2007), The distribution of linear combinations of lattice polynomials from the uniform distribution, submitted.
game-class, Mobius.game-class.
## a capacity
mu <- capacity(c(0,0.1,0.6,rep(0.9,4),1))
## the expectation and the standard deviation
## of the Choquet integral in the uniform case
expect.Choquet.unif(mu)
sd.Choquet.unif(mu)
## the same but empirically
m <- 10000
ch <- numeric(m)
for (i in 1:m) {
f <- runif(3)
ch[i] <- Choquet.integral(mu,f)
}
mean(ch)
sd(ch)
## the expectation and the standard deviation
## of the Choquet integral in the normal case
expect.Choquet.norm(mu)
sd.Choquet.norm(mu)
expect.Choquet.norm(Mobius(mu))
## the same but empirically
for (i in 1:m) {
f <- rnorm(3)
ch[i] <- Choquet.integral(mu,f)
}
mean(ch)
sd(ch)