Description Usage Arguments Details Value Author(s) See Also Examples
Creates an object representing a multivariate Normal-Gamma distribution. If (x,y) has a multivariate Normal-Gamma distribution, then the marginal distribution of y is an Gamma distribution, and the conditional distribution of x given y is multivariate normal.
1 | mnormalgamma(mu=c(0,0), P, alpha, beta)
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mu |
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P |
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alpha |
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beta |
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If (x,y) has a multivariate Normal-Gamma distribution with parameters μ, P, α, and β, then the marginal distribution of y has a Gamma distribution with parameters α, β, and conditionally on y, x has a multivariate normal distribution with expectation μ and precision matrix yP. The probability density is proportional to
f(x,y)=y^{α+k/2-1}\exp(-y(β + (x-μ)^tP(x-μ)/2))
where k is the dimension.
A multivariate Normal-Gamma probability distribution.
Petter Mostad <mostad@chalmers.se>
gamma
,normal
,expgamma
,
normalgamma
, normalexpgamma
,
mnormal
,mnormalexpgamma
1 | plot(mnormalgamma(alpha=3, beta=3))
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Loading required package: MASS
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