pdf.Choquet.unif-methods | R Documentation |
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.
Returns the value of the
p.d.f. or the c.d.f. at y
.
J-L. Marichal and I. Kojadinovic (2007), The distribution of linear combinations of lattice polynomials from the uniform distribution, submitted.
game-class
.
## 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
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