# Poisson Distribution

1. Dec 19, 2015

### aaaa202

1. The problem statement, all variables and given/known data
I am given a data set known to come from a poisson distribution.

2. Relevant equations
Poisson distribution

3. 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?

2. Dec 19, 2015

### BvU

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

3. Dec 19, 2015

### aaaa202

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

4. Dec 19, 2015

### 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.

5. Dec 19, 2015

### haruspex

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.

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