Abstract
This paper considers the Bayesian framework for inference on the parameters of an inverse Gaussian distribution parameterized in terms of the mean (μ) and coefficient of variation (δ). In the past literature, various parameterizations have been considered, some involving the coefficient of variation, where the prior distribution is assumed on the joint parameter (μ, d(δ)), d(.) being some function. However, in some practical applications, the researcher may possess direct prior information about (μ, d(δ)), from some previous studies. Here, we obtain the non-informative prior for (μ, δ) and consider informative priors in terms of (1) independent generalized inverse Gaussian (GIG) priors for μ and δ, and (2) a conditional prior for δ|μ generated by an inverse Gamma prior for δ 2|μ and a GIG prior of μ. Posterior distributions of the parameters μ and δ are derived that are explicitly available except for a normalizing constant. An illustration in terms of a real data example is presented, where the computational algorithm is provided using R software. The resulting values are also checked using the Gibbs sampler using WinBUGS software.
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Acknowledgements
The first author would like to acknowledge the partial support for this research from NSERC of Canada through a Discovery Grant (#RGPIN/4794-2017).
Conflict of Interest Statement On behalf of all authors, the corresponding author states that there is no conflict of interest.
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Appendix
Appendix
1.1 R-codes for the Posterior of CV for the Non-informative Prior
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Chaubey, Y.P., Singh, M., Sen, D. (2021). Bayesian Inference for Inverse Gaussian Data with Emphasis on the Coefficient of Variation. In: Chaubey, Y.P., Lahmiri, S., Nebebe, F., Sen, A. (eds) Applied Statistics and Data Science. CCAS 2021. Springer Proceedings in Mathematics & Statistics, vol 375. Springer, Cham. https://doi.org/10.1007/978-3-030-86133-9_4
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