Brazilian Journal of Probability and Statistics

Some Poisson mixtures distributions with a hyperscale parameter

Stéphane Laurent

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We mainly investigate certain mixtures of Poisson distributions with a scale parameter in the mixing distribution. They help us to derive the bivariate Poisson mixtures arising from the prior and posterior predictive distributions in the semi-conjugate family defined by Laurent and Legrand (ESAIM Probab. Stat. (2011) DOI:10.1051/ps/2010018) for the “two Poisson samples” model, which contains in particular the reference prior when the parameter of interest is the ratio of the two Poisson rates.

Article information

Braz. J. Probab. Stat., Volume 26, Number 3 (2012), 265-278.

First available in Project Euclid: 5 April 2012

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Bayesian model hypergeometric functions Jeffreys prior Poisson mixtures distributions probability generating function reference prior semi-conjugate family of priors


Laurent, Stéphane. Some Poisson mixtures distributions with a hyperscale parameter. Braz. J. Probab. Stat. 26 (2012), no. 3, 265--278. doi:10.1214/11-BJPS139.

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