Method of Moments

**Jontan** · August 6th 2009, 01:15 PM

The PMF of the Poisson distribution is given. E(X) = Lamda and Var(X) = lamda.

Find the method of moments estimator for: lamda with a "^" on top = lamda.

Sorry but I don't know how to add mathematical operators in the post so it would be easier for you to read!

**matheagle** · August 6th 2009, 04:24 PM

In the poisson case you set the sample mean equal to the population mean getting...

$\hat\lambda =\bar X$

**Moo** · August 6th 2009, 11:49 PM

In general, with the method of moments, find the relationship between the moment ( $m_k=\mathbb{E}(X^k)$ ) and the parameter $\lambda$ .

Let's say you have $\lambda=g(m_k)$

Then define $\hat m_k=\frac 1n \sum_{i=1}^n X^k$

You'll have $\hat\lambda=g(\hat m_k)$ and that's all...

Sometimes, you may have a multivariable function : $\lambda=g(m_k,m_p,\dots)$

In which case, it's exactly the same reasoning.

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