# Estimate the mean number of decays

1. Dec 14, 2015

### aaaa202

1. The problem statement, all variables and given/known data
I am given a table of ~3000 measurements for the number of decays from some radioactive substance within some period T. I want to estimate the mean number of decays per period.

2. Relevant equations
Poisson distribution
How to calculate mean.

3. The attempt at a solution
My intuition tells me that the best estimator is simply the to take the arithmetic mean of the dataset. However, given that the data should follow a poisson distribution I am not sure. When is the arithmetic mean the best estimator, and if this is indeed the case, why is it superior to for example fitting to a poisson distribution and then reading of the mean from the fit coefficients?

2. Dec 14, 2015

### insightful

My experience is practical (radioactive waste management) and my intuition is the same as yours.
I'll be interested to see if our intuition is correct.

3. Dec 14, 2015

### haruspex

The search for leased biased estimators is fascinating math, but ignores the real world fact that you need to take into account how the answer will be used. An error one way may be more expensive than the same magnitude of error the other.
Also, taking a Bayesian view, I feel the attempt assumes some property of the a priori distribution of rates, symmetric perhaps.
Anyway, start here: https://en.wikipedia.org/wiki/Bias_of_an_estimator#Estimating_a_Poisson_probability