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Another conjugate family for the normal distribution

Author

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  • Athreya, K. B.

Abstract

It is shown that the family of densities f(z) = czp exp([lambda]1z-1 + [lambda]2z), [lambda]1, [lambda]2 [greater-or-equal, slanted] o, - [infinity] 0, as marginals for the variance gives rise to a new conjugate family for the normal distribution. This family includes the normal gamma family and is minimal in an appropriate sense. This family is known as the generalized inverse Gaussian distribution.

Suggested Citation

  • Athreya, K. B., 1986. "Another conjugate family for the normal distribution," Statistics & Probability Letters, Elsevier, vol. 4(2), pages 61-64, March.
    • Handle: RePEc:eee:stapro:v:4:y:1986:i:2:p:61-64
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    Cited by:

    1. Yanagimoto, Takemi & Ohnishi, Toshio, 2005. "Extensions of the conjugate prior through the Kullback-Leibler separators," Journal of Multivariate Analysis, Elsevier, vol. 92(1), pages 116-133, January.
    2. Hannes Leeb & Paul Kabaila, 2017. "Admissibility of the usual confidence set for the mean of a univariate or bivariate normal population: the unknown variance case," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 801-813, June.

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