Mixture of the Riesz Distribution with Respect to a Multivariate Poisson

References

• Aalen , O. O. ( 1992 ). Modelling heterogeneity in survival analysis by the compound Poisson distribution . Ann. Appl. Probab. 2 : 951 – 972 .
   Google Scholar
• Abramowitz , M. , Stegum , I. A. ( 1974 ). Handbook of Mathematical Functions . New York : Dover .
   Google Scholar
• Andersson , S. A. , Klein , T. ( 2010 ). On Riesz and Wishart distributions associated with decomposable undirected graphs . J. Multivariate Anal. 101 ( 4 ): 789 – 810 .
   Web of Science ®Google Scholar
• Ben Farah , M. , Hassairi , A. ( 2007 ). Characterization of the Dirichlet distribution on symmetric matrices . Statist. Probab. Lett. 77 : 357 – 364 .
   Web of Science ®Google Scholar
• Boutouria , I. ( 2009 ). Characterization of the Wishart distribution on homogeneous cones in the Bobecka and Wesolowski way . Commun. Statist. Theory Meth. 38 : 2552 – 2566 .
   Web of Science ®Google Scholar
• Bromet , E. J. , Feinberg , S. E. , Follman , D. , Lambert , D. , May , S. M. ( 1985 ). Longitudinal analysis of categorical epidemiological data: A study of three mile Island . Environ. Health Perspet. 63 : 241 – 248 .
   PubMedGoogle Scholar
• Davis , C. J. , Liu , C. , Zhang , L. ( 2004 ). A mixture model-based approach to the classification of ecological habitats using forest inventory and analysis data . Can. J. Forest. Res. 34 : 1150 – 1156 .
   Web of Science ®Google Scholar
• Diebolt , J. , Robert , C. P. ( 1994 ). Estimation of finite mixture distributions by Bayesian sampling . J. Roy. Statist. Soc. 56 : 363 – 375 .
   Google Scholar
• Faraut , J. , Korányi , A. (1994). Analysis on Symmetric Cones . Oxford : Oxford University Press.
   Google Scholar
• Feller , W. ( 1971 ). An Introduction to Probability Theory and Its Applications . vol. I and II. 2nd ed. New York : Wiley .
   Google Scholar
• Foll , R. , Gongora , M. A. , Hines , E. L. , Morgan , D. W. ( 2005 ). Evolving fuzzy mixture models: Applications in anaesthesia . Proc. 3rd IASTED Int. Conf. Biomed. Eng. 5 : 596 – 601 .
   Google Scholar
• Formann , A. K. , Kohlmann , T. ( 1996 ). Latent class analysis in medical research . Statist. Meth. Med. Res. 5 : 179 – 211 .
   PubMedGoogle Scholar
• Gindikin , S. G. ( 1964 ). Analysis on homogeneous domains . Russ. Math. Surv. 29 : 1 – 89 .
   Google Scholar
• Harris , C. M. , Singpurwalla , N. D. ( 1968 ). Lifes distributions derived from stochastic hazard functions . IEEE Trans. Reliab. 17 : 70 – 79 .
   Web of Science ®Google Scholar
• Hassairi , A. , Lajmi , S. ( 2001 ). Riesz exponential families on symmetric cones . J. Theoret. Probab. 14 ( 4 ): 927 – 948 .
   Web of Science ®Google Scholar
• Hassairi , A. , Lajmi , S. , Zine , R. ( 2005 ). Beta-Riesz distributions on symmetric cones . J. Statist. Plann. Infer. 133 : 387 – 404 .
   Web of Science ®Google Scholar
• Hassairi , A. , Lajmi , S. , Zine , R. ( 2007 ). Riesz inverse Gaussian distributions . J. Statist. Plann. Infer. 137 : 2024 – 2033
   Web of Science ®Google Scholar
• Hassairi , A. , Louati , M. ( 2009 ). Multivariate stable exponential families and Tweedie scale . J. Statist. Plann. Infer. 139 : 143 – 158 .
   Web of Science ®Google Scholar
• Hassairi , A. , Masmoudi , M. , Zine , R. ( 2009 ). On the projections of the Dirichlet probability distribution on symmetric cones . J. Math. Anal. Appl. 349 ( 2 ): 367 – 373 .
   Web of Science ®Google Scholar
• Hill , D. L. , Laud , P. W. , Saunders , R. ( 1980 ). Maximum likelihood estimation for mixtures . Can. J. Statist. 8 : 87 – 93 .
   Google Scholar
• Johnson , L. L. , Kemp , A. W. , Kotz , S. ( 2005 ). Univariate Discrete Distributions. , 3rd ed. Hoboken , NJ : Wiley .
   Google Scholar
• Jørgensen , B. ( 1997 ). The Theory of Dispersion Models. , 1st ed. London : Chapman & Hall .
   Google Scholar
• Karlis , D. , Meligkotsidou , L. ( 2007 ). Finite mixtures of multivariate Poisson distributions with application . J. Statist. Plann. Infer. 137 : 1942 – 1960 .
   Web of Science ®Google Scholar
• Laird , N. M. ( 1978 ). Empirical Bayes methods for two-way contingency tables . Biometrika 65 : 581 – 590 .
   Web of Science ®Google Scholar
• Lebedev , N. N. ( 1972 ). Special Functions and Their Applications . New York : Dover Publications, Inc. Translated and edited by Richard Silverman .
   Google Scholar
• Letac , G. ( 1992 ). Lectures on natural exponential families and their variance functions. Monografias de Matemática. Vol. 50. Rio de Janeiro: IMPA .
   Google Scholar
• Liang , K. Y. , Rathouz , P. J. ( 1999 ). Hypothesis testing under mixture models: Application to genetic linkage analysis . Biometrics 55 ( 1 ): 65 – 74 .
   PubMed Web of Science ®Google Scholar
• Liu , C. , Xie , J. , Zhang , Y. ( 2007 ). Weighted nonparametric maximum likelihood estimate of a mixing distribution in non randomized clinical trials . Statist. Med. 26 ( 29 ): 5303 – 5319 .
   PubMed Web of Science ®Google Scholar
• Perline , R. ( 1988 ). Mixed Poisson distributions tail equivalent to their mixing distributions . Statist. Probab. Lett. 38 : 229 – 233 .
   Web of Science ®Google Scholar
• Seshadri , V. ( 1994 ). The Inverse Gaussian Distribution. A Case Study in Exponential Families . Oxford : Oxford University Press .
   Google Scholar
• Stigler , S. M. ( 1986 ). The History of Statistics . Cambridge , MA : Belknap Press of Harvard University Press .
   Google Scholar