check.commonprob(commonprob)
commonprob
| Matrix of pairwise probabilities. |
commonprob[i,i]
are interpreted as
probabilities p(A_i) that a binary variable A_i
equals 1. The
off-diagonal elements commonprob[i,j]
are the probabilites
p(A_iA_j) that both A_i and A_j are 1.
This programs checks some necessary conditions on these probabilities which must be fulfilled in order that a joint distribution of the A_i with the given probabilities can exist.
The conditions checked are
0 <= p(A_i) <= 1
max(0, p(A_i)+p(A_j)-1) <= p(A_iA_j) <= min(p(A_i), p(A_j)), i != j
p(A_i)+p(A_j)+p(A_k)-p(A_iA_j)-p(A_iA_k)-p(A_jA_k) <= 1, i != j, i != k, j != k
check.commonprob
returns TRUE
, if all conditions are
fulfilled. The attribute "message"
of the return value contains
some information on the errors that were found.simul.commonprob
commonprob2sigma
check.commonprob(cbind(c(0.5, 0.4), c(0.4, 0.8))) check.commonprob(cbind(c(0.5, 0.25), c(0.25, 0.8))) check.commonprob(cbind(c(0.5, 0, 0), c(0, 0.5, 0), c(0, 0, 0.5)))