Abstract
In this paper, we propose a new conjugate prior probability distribution to many likelihoods distributions. In particular, we use the weighted Lindley distribution as a conjugate prior distribution. The weighted Lindley distribution can be viewed as a mixture of two gamma distributions with know weights. The weighted Lindley distribution of conjugate priors offers a more flexible class of priors than the class of gamma prior distributions. The results are illustrated for the problem of inference for Poisson and normal parameters.
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Acknowledgements
I thank the two anonymous referees and an associate editor for the constructive suggestions and comments.
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Appendix. R script
Appendix. R script
The following algorithm calculate the Bayesian estimates of the Poisson parameter.
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Bourguignon, M. An Alternative Conjugate Prior Distribution for Positive Parameters. Ann. Data. Sci. 6, 237–243 (2019). https://doi.org/10.1007/s40745-018-0174-z
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DOI: https://doi.org/10.1007/s40745-018-0174-z