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TitleA regional poisson model
Publication TypeJournal Article
Year of Publication2015
AuthorsWithers, C.S., and Nadarajah S.
JournalMathematical Scientist
Pagination23 - 28
Date Published2015
ISSN03123685 (ISSN)
KeywordsAIDS, confidence interval, Maximum likelihood, Maximum likelihood estimate, Maximum likelihood estimation, Poisson model, Regions, Sufficient statistics
AbstractSuppose that we observe independent Poisson variables {Ni,t, 1 , i,t] = pimt(θ), where p = (p1.p1)T are unknown probabilities adding to 1 and mt(θ) is a given function of an unknown parameter θ in ℝq. Then the marginal totals of the observations form a sufficient statistic. We obtain maximum likelihood estimates of p and θ. their approximate covariance, and hence an approximate confidence interval for any function of these parameters, in particular for E[Ni,t] and E[∑s= 1t Ni,s] at some future time t. Applications are made to modelling regional AIDS cases. © Applied Probability Trust 2015.

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