Ioannis Ntzoufras

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Bayesian estimation in Kibble's bivariate gamma distribution

G.  Iliopoulos, D. Karlis and I.  Ntzoufras (2005)

Canadian Journal of Statistics, 33 (4) ,  571-589.

 

ABSTRACT

The paper describes Bayesian estimation for the parameters of Kibble's  (1941) bivariate gamma distribution. The density of this distribution can be written as a mixture, allowing for a simple data augmentation scheme. An MCMC algorithm is constructed to facilitate Bayesian estimation. We show that the resulting chain is geometrically ergodic and thus a regenerative sampling procedure is applicable allowing for estimation of ergodic means' standard errors. Bayesian hypothesis testing procedures are developed to test both the dependence hypothesis of the two variables as well as the hypothesis that their means are equal. A reversible jump MCMC algorithm is proposed to carry out this model selection problem. Real and simulated datasets are used to illustrate the proposed methodology.

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Last revised: 23/11/2011