|Parameters|| location (real)
In probability theory and statistics, the normal-inverse-gamma distribution (or Gaussian-inverse-gamma distribution) is a four-parameter family of multivariate continuous probability distributions. It is the conjugate prior of a normal distribution with unknown mean and variance.
has an inverse gamma distribution. Then has a normal-inverse-gamma distribution, denoted as
It is also possible to let in which case the pdf becomes
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Generation of random variates is straightforward:
- Sample from an inverse gamma distribution with parameters and
- Sample from a normal distribution with mean and variance
- The normal-gamma distribution is the same distribution parameterized by precision rather than variance
- A generalization of this distribution which allows for a multivariate mean and a positive-definite covariance matrix is the normal-inverse-Wishart distribution
- Dominici, Francesca; Giovanni Parmigiani, Merlise Clyde (2000-09). "Conjugate Analysis of Multivariate Normal Data with Incomplete Observations". The Canadian Journal of Statistics / La Revue Canadienne de Statistique (The Canadian Journal of Statistics / La Revue Canadienne de Statistique, Vol. 28, No. 3) 28 (3): 533–550. doi:10.2307/3315963. JSTOR 3315963.
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