Definition
For a pair of random variable, (X,T), suppose that the conditional distribution of X given T is given by
where this mean that the condition distribution is a normal distribution with mean and precision — equivalently, with variance
Suppose also that the marginal distribution of T is given by
where this means that T has a gamma distribution. Here λ, α and β are parameters of the joint distribution.
Then (X,T) has a normal-gamma distribution, and this is denoted by
Read more about this topic: Normal-gamma Distribution
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