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Maximum likelihood estimator

  1. Feb 22, 2005 #1
    Maximum likelihood estimator....

    ok, i'm stil a bit lost...so tell me if this is right:

    [tex] f_y(y;\theta) = \frac{2y}{\theta^2}, for 0 < y < \theta [/tex]

    find the MLE estimator for theta.

    [tex] L(\theta) = 2yn\theta^{-2 \sum_1^n y_i [/tex].

    is this even right to begin with?

    then take the natural log

    [tex]ln2yn + -2\sum_1^n y_i * ln\theta[/tex]

    take derivative

    [tex]\frac {1}{2yn} -\frac{ 2 * \sum_1^n yi}{\theta}. [/tex]

    now how do I solve this in terms of theta? and after that, what do I do next?

    this just doesnt look right

    and I also need to find it using the method of moments, but I get [tex]\frac {y^4}{2\theta} [/tex] after the integral...

    and this one too...this looks too messy:

    [tex]fy(y;\theta) = \frac{y^3e^{\frac{-y}{\theta}}}{6\theta^4} [/tex]
    Last edited: Feb 22, 2005
  2. jcsd
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