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Math Help - Maximum Likelihood estimator

  1. #1
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    Maximum Likelihood estimator

    Can someone please show me how to do this question
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  2. #2
    Grand Panjandrum
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    Re: Maximum Likelihood estimator

    Quote Originally Posted by jonnyl View Post
    Can someone please show me how to do this question
    Given an observation u>0 of Y the likelihood of \theta is:

    l(\theta|u)=2u\theta e^{-\theta u^2}

    and this is a maximum when:

    \frac{\partial}{\partial \theta}l(\theta|u)=0

    which you solve for \theta in terms of u to get the maximum likelihood estimator.

    If you have a sample of size bigger than one, the likelihood is the product of the individual sample value likelihoods, and it will be easier to maximise the log likelihood, but that will give the same result as maximising the likelihood.

    CB
    Last edited by CaptainBlack; September 3rd 2011 at 03:42 AM.
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