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Thread: help on statistics needed please help

  1. #1
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    help on statistics needed please help

    Consider a random sample of size n from a distribution with pdf


    $\displaystyle f(x;q)=(Ln(q))^x/qx!$ if $\displaystyle x=0,1,...$ and $\displaystyle q>1 $and $\displaystyle 0$ otherwise.

    a)Find a complete sufficient statistic for$\displaystyle q$

    b)Find the maximum likelihood estimator of $\displaystyle q$

    c)Find the Cramer-Rao Lower Bound for $\displaystyle q$

    d)Find the Uniformly Minimum Variance Unbiased Estimator for $\displaystyle Ln(q)$

    e)Find the Uniformly Minimum Variance Unbiased Estimator for $\displaystyle (Ln(q))^2$

    (f) Find the Cramer-Rao Lower Bound for $\displaystyle (Ln(q))^2$



    please help solve these questions
    Last edited by Kat-M; May 2nd 2009 at 07:10 PM. Reason: put wrong notation
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  2. #2
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    part a

    for part a) can be writen as$\displaystyle 1/qx!e^{xLn(Ln(q))}$which shows that this is regular exponent. and by Theorem, we know $\displaystyle S=\Sigma X$ is complete suff stat. But how do we find the MLE of q?
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  3. #3
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    need some help on this please

    for the part b) Find the maximum likelihood estimator of . i found that MLE of$\displaystyle q=e^{\overline{X}}$ where$\displaystyle \overline{X}=\Sigma X/n$. and now i am trying to do part c)Find the Cramer-Rao Lower Bound for . A theorem tells me that (i hope this is correct) to find CRLB of $\displaystyle q$, find $\displaystyle Var(e^{\overline{X}})$.
    Can anyone help me compute it? i dont know how.
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