# conditional distribution

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## conditional distribution

[kən′dish·ən·əl dis·trə′byü·shən]
(statistics)
If W and Z are random variables with discrete values w1, w2,…, and z1, z2,…, the conditional distribution of W given Z = z is the distribution which assigns to wi, i = 1,2,…, the conditional probability of W = wi given Z = z.
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Each root node has prior probabilities and the conditional probability distribution (CPD) should be specified for each child node in the BNs.
The conditional probability distribution for each node can be written as:
Estimation of the conditional probability distribution provides the basis for the probabilistic forecasts.
Table 2 summarizes the conditional probability distributions of R.
To further evaluate the out-of-sample performance of the conditional probability distributions, we use the 10-year rolling-window procedure described previously.
Specifically, for a node X having k states, an independent Dirichlet distribution on k parameters is associated with each parent configuration in the conditional probability distributions P(X | pa(X)).

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