R: Distribution of the Choquet integral for evaluations...
pdf.Choquet.unif-methods
R Documentation
Distribution of the Choquet integral for evaluations uniformly
distributed on the unit hypercube
Description
Methods for computing the probability density and cumulative
distribution functions of the Choquet integral with respect to a game
for evaluations uniformly distributed on the unit hypercube.
Methods
object = "game", y = "numeric"
Returns the value of the
p.d.f. or the c.d.f. at y.
References
J-L. Marichal and I. Kojadinovic (2007), The distribution of linear
combinations of lattice polynomials from the uniform distribution,
submitted.
See Also
game-class.
Examples
## a capacity
mu <- capacity(c(0,0.1,0.6,rep(0.9,4),1))
## the cdf of the Choquet integral at 0.7
cdf.Choquet.unif(mu,0.7)
## the same but empirically
m <- 10000
ch <- numeric(m)
for (i in 1:m) {
f <- runif(3)
ch[i] <- Choquet.integral(mu,f)
}
sum(ifelse(ch<=0.7,1,0))/m