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Finite mixture of gamma distributions: a conjugate prior. (English) Zbl 1162.62323

Summary: A finite mixture of \(\gamma\) distributions is used as a conjugate prior, which gives a nice form of posterior distributions. This class of conjugate priors offers a more flexible class of priors than the class of \(\gamma\) prior distributions. The usefulness of a mixture of \(\gamma\)-type priors and the posteriors of uncertain parameters \(\lambda \) for the Poisson distribution are illustrated by using a Markov Chain Monte Carlo (MCMC), Gibbs sampling approach, on hierarchical models. Using generalized hypergeometric functions, the method to approximate maximum likelihood estimators for the parameters of S.K. Agarwal and J.A. Al-Saleh’s [Generalized gamma type distribution and its hazard rate function. Commun. Stat., Theory Methods 30, No. 2, 309–318 (2001; Zbl 0993.62005)] generalized gamma-type distribution is also suggested.

MSC:

62F15 Bayesian inference
62E15 Exact distribution theory in statistics
65C40 Numerical analysis or methods applied to Markov chains
33C90 Applications of hypergeometric functions

Citations:

Zbl 0993.62005
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References:

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