Some aspects of statistical inference on the lagrange (generalized) poisson distribution |
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| Authors: | M. M. Shoukri I.U.H. Mian |
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| Affiliation: | 1. Department of Population Medicine , University of Guelph, Ontario, Canada Statistics Canada , Ottawa, Canada;2. Department of Population Medicine , University of Guelph Ontario, Canada Statistics Canada , Ottawa, Canada |
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| Abstract: | A generalization of the Poisson distribution was defined by Consul and Jain (Ann. Math. Statist., 41, (1970)) and was obtained as a particular family of Lagrange distributions by Consul and Shenton (SIAM. J. Appl. Math., 23, (1972)). The distribution is subsequently named the generalized Poisson distribution (GPD). This GPD reduces to the Poisson distribution for ? = 0. When the data have a one-way layout structure, the asymptotically locally optimal Neyman's C(d) test is constructed and compared with the conditional test on the hypothesis Ho? = 0. Within the framework of the generalized linear models an appropriate link function is given, and the asymptotic distributions of the estimated parameters are derived. |
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| Keywords: | Lagrange expansion Generalized Poisson distribution Asymptotic inference Linear exponential family |
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