Aniticipating Operator

The associativity of the operator of composition would be desirable not only to meet the requirements of mathematical beauty, but also to make the design of computational algorithms easier. Its lack is, in a way, compensated by the existence of a generalized operator of composition, which is called an anticipating operator.

anticipate(kappa, lambda, M)

Arguments

kappa	Distribution \(\kappa\)
lambda	Distribution \(\lambda\)
M	vector of variables, which is essential for anticipating operator \(\diamond_M\)

Value

Distribution \(\kappa \diamond_M \lambda\)

Details

Consider an arbitrary set of variables M and two distributions \(\kappa(K)\), \(\lambda(L)\). Their anticipating composition is given by the formula $$\kappa \diamond_M \lambda = (\lambda^{\downarrow (M\setminus K)\cap L} \cdot \kappa) \triangleright \lambda.$$ The operator \(\diamond_M\) is called an anticipating operator of composition. Notice, it is a generalization of the operator of composition in the sense that $$\kappa \diamond_\emptyset \lambda = \kappa \triangleright \lambda.$$

See also

multiply, compose, Distribution

Examples

Pi <- Distribution("Pi");
K <- Distribution("K");
#load Data to the Distributions..

K1 <- c("A", "B");

newDist <- anticipate(Pi,K,K1);
getData(newDist);
#> NULL