A hand-sized Poisson rate estimate

Question

Over five minutes you count events: 2, 3, 1, 4, 0. You model the counts as Poisson with rate \lambda, whose mean is \lambda. Use the method of moments to estimate \lambda.

Accepted Answer

Step 1: the sample average. Add the counts and divide by five: \bar X = \frac{2 + 3 + 1 + 4 + 0}{5} = \frac{10}{5} = 2. Step 2: match the mean. The Poisson mean is \lambda, so \hat\lambda = \bar X = 2 events per minute. All there is to it. With one parameter, match the mean; for the Poisson the mean is the rate, so the estimate is the average count. Takeaway. Average the counts to get the rate: \hat\lambda = 10/5 = 2.

A hand-sized Poisson rate estimate

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