International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 1, Pages 193-196
doi:10.1155/S0161171285000205
A note on the estimation of the Poisson parameter
Department of Management and Marketing, Illinois State University, Normal 61761, Illinois, USA
Received 19 August 1983
Copyright © 1985 S. S. Chitgopekar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
This paper considers the problem of estimating the mean of a Poisson
distribution when there are errors in observing the zeros and ones and obtains both the maximum likelihood and moments estimates of the Poisson mean and the error probabilities. It is interesting to note that either method fails to give unique estimates of these parameters unless the error probabilities are functionally related. However, it is equally interesting to observe that the estimate of the Poisson mean does not depend on the functional relationship between the error probabilities.