Estimate the mean number of decays

[aaaa202]

Homework Statement

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.

Homework Equations

Poisson distribution
How to calculate mean.

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?

 

[insightful]

My intuition tells me that the best estimator is simply the to take the arithmetic mean of the dataset.

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.

 

[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