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Math Help - MLE problem

  1. #1
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    MLE problem

    find the MLE of the iid random variables of uniform distribution U(2\theta,3\theta) where  \theta>0
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  2. #2
    MHF Contributor matheagle's Avatar
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    Obtain the max of

    {1\over \theta^n}I(2\theta<X_{(1)}<X_{(n)}<3\theta)

    where those are order stats and the I is an indicator function.
    I had thought there would be two competing solutions, but the answer is quite simple.
    Last edited by matheagle; February 25th 2010 at 08:22 AM.
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  3. #3
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    Quote Originally Posted by matheagle View Post
    Obtain the max of

    {1\over \theta^n}I(2\theta<X_{(1)}<X_{(n)}<3\theta)

    where those are order stats and the I is an indicator function.
    I had thought there would be two competing solutions, but the naswer is quite simple.
    i think the answer is (\frac {X_{(1)}}{2},\frac{X_{(n)}}{3})
    but i do not know whether it is true?
    Last edited by chialin4; February 25th 2010 at 08:50 AM.
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  4. #4
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by chialin4 View Post
    i think the answer is (\frac {X_{(n)}}{2},\frac{X_{(1)}}{3})
    but i do not know whether it is true?
    neither, and the answer is not an interval.
    you want theta as small as possible and that is \frac {X_{(n)}}{3}
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  5. #5
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    Quote Originally Posted by matheagle View Post
    neither, and the answer is not an interval.
    you want theta as small as possible and that is \frac {X_{(n)}}{3}
    but we do not know whether \frac {X_{(n)}}{3} is greater than \frac {X_{(1)}}{2} or not~
    so which one should we chose?
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  6. #6
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by chialin4 View Post
    but we do not know whether \frac {X_{(n)}}{3} is greater than \frac {X_{(1)}}{2} or not~
    so which one should we chose?

    \frac {X_{(n)}}{3}<\theta<\frac {X_{(1)}}{2}
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  7. #7
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    Quote Originally Posted by matheagle View Post
    \frac {X_{(n)}}{3}<\theta<\frac {X_{(1)}}{2}
    so MLE is \frac {X_{(n)}}{3}?
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