Bayesian estimation in Kibble's bivariate
gamma distribution
George Iliopoulos, Dimitris Karlis and Ioannis Ntzoufras
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 the standard errors of the
ergodic means. 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.
Key words and phrases: Downton's bivariate exponential distribution;
Kibble's bivariate gamma distribution; Markov chain