Abstract
The problem of identification of uniform mixtures via posterior means is studied. For linear posterior means a complete solution is given. It determines a family of prior distributions involving beta of both kinds and gamma. Identifiability via any consistent posterior mean is also investigated.
Similar content being viewed by others
REFERENCES
Arnold, B. C., Castillo, E. and Sarabia, J. M. (1993). Conditionally specified models: Structure and inference, Multivariate Analysis: Future Directions 2 (eds. C. M. Cuadras and C. R. Rao), 441–450, Elsevier, Amsterdam.
Barndorff-Nielsen, O. (1965). Identifiability of mixtures of exponential families, J. Math. Anal. Appl., 12, 115–121.
Cacoullos, T. and Papageorgiou, H. (1983). Characterizations of discrete distributions by a conditional distribution and a regression function, Ann. Inst. Statist. Math., 35, 95–103.
Cacoullos, T. and Papageorgiou, H. (1984). Characterizations of mixtures of continuous distributions by their posterior means, Scand. Actuar. J., 8, 23–30.
Korwar, R. M. (1975). On characterizing some discrete distributions by linear regression, Comm. Statist., 4, 1133–1147.
Korwar, R. M. (1977). On characterizing Lagrangian-Poisson and quasi-binomial distributions, Comm. Statist., 6, 1409–1416.
Kotz, S. and Steutel, F. W. (1988). Note on a characterization of exponential distributions, Statist. Probab. Lett., 6, 201–203.
Krishnaji, N. (1974). Characterization of some discrete distributions based on a damage model, Sankhyā, Ser. A, 36, 204–213.
Mathai, M. A. and Moschopoulos, P. G. (1992). A form of multivariate gamma distribution, Ann. Inst. Statist. Math., 44, 97–106.
Papageorgiou, H. (1984a). Characterizations of multinomial and negative multinomial mixtures by regression, Austral. J. Statist., 26, 25–29.
Papageorgiou, H. (1984b). Characterizations of continuous binomial and negative binomial mixtures, Biometrical J., 26, 795–798.
Papageorgiou, H. (1985). On characterizing some discrete distributions by a conditional distribution and a regression function, Biometrical J., 27, 473–479.
Patil, G. P. and Bildikar, S. (1966). Identifiability of countable mixtures of discrete probability distributions using methods of infinite matrices, Proceedings of the Cambridge Philosophical Society, 62, 485–494.
Teicher, H. (1961). Identifiability of mixtures, Ann. Math. Statist., 32, 244–248.
Wesolowski, J. (1994). Bivariate distributions via a second kind beta conditional distribution and a regression function, Journal of Mathematical Sciences (to appear).
Wesolowski, J. (1995a). Bivariate distributions via a Pareto conditional distribution and a regression function, Ann. Inst. Statist. Math., 47, 177–183.
Wesolowski, J. (1995b). Bivariate discrete measures via power series conditional distribution and a regression function, J. Multivariate Anal., 55, 219–229.
Author information
Authors and Affiliations
About this article
Cite this article
Gupta, A.K., Wesolowski, J. Uniform Mixtures Via Posterior Means. Annals of the Institute of Statistical Mathematics 49, 171–180 (1997). https://doi.org/10.1023/A:1003175024895
Issue Date:
DOI: https://doi.org/10.1023/A:1003175024895