Abstract
In this paper, we are concerned with identification of a discrete uniform mixture by the posterior mean. An exact formula for a prior distribution is given. Also some examples featuring negative binomial, negative hypergeometric and beta-Pascal distributions are provided.
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Arnold, B.C., E. Castillo and J.M. Sarabia (1993). Conditionally specified models: structure and inference. InMultivariate Analysis: Future Directions, 2 (C.M. Cuadras and C.R. Rao eds.) Elsevier, Amsterdam, 441–450.
Cacoullos, T. and H. Papageorgiou (1983). Characterizations of discrete distributions by a conditional distribution and a regression function.Annals of the Institute of Statistical Mathematics,35, 95–103.
Gupta, A.K. and J. Wesoŀowski (1997). Uniform mixtures via posterior means.Annals of the Institute of Statistical Mathematics,49, 171–180.
Gupta, A.K. and J. Wesoŀowski (1998). Regressional identifiability and identification for beta mixtures. Technical Report No. 98-13. Department of Mathematics and Statistics, Bowling Green State University, 1–10.
Korwar, R.M. (1975). On characterizing some discrete distributions by linear regression.Communications in Statistics,4, 1133–1147.
Korwar, R.M. (1977). On characterizing Lagrangian-Poisson and quasi-binomial distributions.Communications in Statistics,6, 1409–1416.
Krishnaji, N. (1974). Characterization of some discrete distributions based on a damage model.Sankhyã, A,36, 204–213.
Kyriakoussis, A. and H. Papageorgiou (1991). Characterizations of logarithmic series distributions.Statistica Neerlandica,45, 1–8.
Ord, J.K. (1972).Families of Frequency Distributions. Hafner Publishing Company, New York.
Papageorgiou, H. (1985). On characterizing some discrete distributions by a conditional distribution and a regression function.Biometrical Journal,27, 473–479.
Papageorgiou, H. and J. Wesoŀowski (1997). Posterior mean identifies the prior distribution in NB and related models.Statistics and Probability Letters,36, 127–134.
Patil, G.P. and S. Bildikar (1966). Identifiability of countable mixtures of discrete probability distributions using methods of infinite matrices.Proceedings of the Cambridge Philosophical Society,62, 485–494.
Patil, G.P. and V. Seshadri (1964). Characterization theorems for some univariate probability distributions.Journal of the Royal Statistical Society, B,26, 286–292.
Sapatinas, T. (1985). Identifiability of mixtures of power series distributions and related characterizations.Annals of the Institute of Statistical Mathematics,47, 447–459.
Titterington, D.M., A.F.M. Smith, and U.E. Makov (1985).Statistical Analysis of Finite Mixture Distributions. Wiley, New York.
Wesoŀowski, J. (1995a). Bivariate distributions via a Pareto conditional distribution and a regression function.Annals of the Institute of Statistical Mathematics,47, 177–183.
Wesoŀowski, J. (1995b). Bivariate discrete measures via a power series conditional distribution and a regression function.Journal of Multivariate Analysis,55, 219–229.
Wesoŀowski, J. (1996). A new conditional specification of the bivariate Poisson conditionals distribution.Statistica Neerlandica,50, 390–393.
Xekalaki, E. (1981). A characterization of the negative hypergeometric distribution based on conditional expectation. InProceedings of the Sixth Conference on Probability Theory (B. Bercanu, S. Grigorescu, M. Iosifescu, and T. Postelnicu eds.) Editura Academici Republicii Socialiste Romania, Bucuresti, 379–384.
Xekalaki, E. (1983). Infinite divisibility, completeness and regression properties of the univariate generalized Waring distribution.Annals of the Institute of Statistical Mathematics,35, 279–289.
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Gupta, A.K., Wesoŀowski, J. Discrete uniform mixtures via posterior means. Test 8, 399–409 (1999). https://doi.org/10.1007/BF02595877
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DOI: https://doi.org/10.1007/BF02595877
Key words
- Beta-Pascal distribution
- discrete uniform distribution
- identification of mixtures
- mixture
- negative binomial distribution
- negative hypergeometric distribution
- posterior mean