kappalab (version 0.4-12)

pdf.Choquet.unif-methods: 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