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Math Help - moments estimators

  1. #1
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    moments estimators

    Let S=(1,2,3,4,5,6,7,8) be a random sample of independent values from a Binomial distribution B(250,P) with unknown p.
    Find the moments estimator for p.
    Some hints about that. or does 250 matters in this question ?
    Last edited by mr fantastic; March 13th 2010 at 05:01 PM. Reason: Restored deleted question. Thread closed as per SOP.
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  2. #2
    MHF Contributor matheagle's Avatar
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    The method of moments estimator sets the sample mean equal to the population mean.
    So, in a way you have two n's.
    By the way, that data doesn't look like it would come from a Bin(250,p).

    But what you should do is compute the sample mean of 1 through 8
    which is (8)(9)/2=45 divided by 8 or 4.5 and set that equal to 250p and solve for p.

    Thus \hat P=4.5/250=.018

    This data is hardly from a bin(250,p) distribution.
    Maybe more of a Poisson.
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  3. #3
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    Quote Originally Posted by matheagle View Post
    The method of moments estimator sets the sample mean equal to the population mean.
    So, in a way you have two n's.
    By the way, that data doesn't look like it would come from a Bin(250,p).

    But what you should do is compute the sample mean of 1 through 8
    which is (8)(9)/2=45 divided by 8 or 4.5 and set that equal to 250p and solve for p.

    Thus \hat P=4.5/250=.018

    This data is hardly from a bin(250,p) distribution.
    Maybe more of a Poisson.
    but is the estimator you find is biased or unbiased?
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  4. #4
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    Quote Originally Posted by fyw891105 View Post
    but is the estimator you find is biased or unbiased?
    Take an expected value and see for yourself The estimator is a nice, linear function of your sample: <br />
\sum_{i = 1} ^ 8 \frac{S_i}{(8)(250)}<br />
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  5. #5
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    I found this is biased because expectation rather than p is P/250.
    Am I correct ?
    thank you
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