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Maximum Likelihood Estimation from Grouped Poisson Data

Walter H. Carter, Jr., Jacob Van Bowen, Jr. and Raymond H. Myers
Journal of the American Statistical Association
Vol. 66, No. 334 (Jun., 1971), pp. 351-353
DOI: 10.2307/2283935
Stable URL: http://www.jstor.org/stable/2283935
Page Count: 3
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Maximum Likelihood Estimation from Grouped Poisson Data
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Abstract

In this article, sufficient conditions are given for the existence of a unique solution of the likelihood equation which results from a grouped data sample. The necessary and sufficient conditions for the convergence of a sequence defined by the method of successive approximations to this unique solution are also given. Finally, it is shown that when the groups from an underlying Poisson distribution are connected the method of successive approximations will converge to the unique solution of the resulting likelihood equation regardless of the starting value chosen provided that the sample is not concentrated entirely in either or both the first and last groups.

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