Poisson Distrib.: Estimating Mean of Data Set

[aaaa202]

Homework Statement

I am given a data set known to come from a poisson distribution.

Homework Equations

Poisson distribution

The Attempt at a Solution

I want to calculate the mean of the data set for use in the Poisson Distribution function. How do I best estimate this. Do I take the arithmetic average of the data set or do I fit to a Poissonian? Which is the better estimator for the true mean?

 

[BvU]

well, why not do both and compare the results ? There is a small subtle difference, but it may go unnoticed in many cases.

 

[aaaa202]

I just want to know which is closer to the correct result, i.e. the parameter for the true distribution.

 

[BvU]

You've been around long enough to know PF requires an effort from your side too. What is the exact problem formulation ?
What is the context of the exercise (intro, hypothesis testing, chi-squared, other?)
You are supposed to have sufficient knowledge of the matter at hand to do this exercise -- so if this is just additional curiosity, do the exercise first. And if it's part of the exercise, then an attempt at solution is required by PF rules before assistance can be given.

 

[haruspex]

I just want to know which is closer to the correct result, i.e. the parameter for the true distribution.

That's not an answerable question. Sometimes one will be closer, sometimes the other. What you can ask is which produces an unbiased result, i.e. no consistent tendency to underestimate or overestimate.
Even then, this might not be the best in practice. It depends what you will do with the answer. In some contexts, it may be much more costly to overestimate than to underestimate, say. A full solution involves a cost function, and, no doubt, Bayesian analysis.