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Math Help - Maxiumum Likelihood function

  1. #1
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    Maxiumum Likelihood function

    observations 1,2,...n are made from a distribution with the following pdf:
    f(x)=theta/x^(theta+1)

    find an expression for theta hat.
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  2. #2
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    Starting from the definition of the liklihood function, you end up with \frac{\theta ^ n}{\prod _{i = 1} ^ n x_i ^ {\theta + 1}}. From there, the trick should be to maximize the log of this guy, which is a pretty standard thing to do. In most cases, maximizing a function is equivalent to maximizing its log. I ended up with \hat{\theta} = \frac{n}{\sum _ {i = 1} ^ n \mbox{log}(x_i)} if I did it right.
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  3. #3
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    Quote Originally Posted by scubasteve123 View Post
    observations 1,2,...n are made from a distribution with the following pdf:
    f(x)=theta/x^(theta+1)

    find an expression for theta hat.
    You will find several examples in this subforum of how to find a maximum likelihood estimate. I suggest you find them (use the Search tool) and review them.
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