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.
Returns the expectation or the standard deviation of the Choquet integral.
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)