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Math Help - Method of Moments

  1. #1
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    Method of Moments

    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!
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  2. #2
    MHF Contributor matheagle's Avatar
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    In the poisson case you set the sample mean equal to the population mean getting...

    \hat\lambda =\bar X
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  3. #3
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    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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