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)