A Note On the Estimation of the Poisson Parameter

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.

Keywords

• Poisson distribution
• estimation
• observation errors.