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Unbiased estimator for The exponential

  1. Dec 23, 2011 #1
    Looking at obtaining the unbiased estimator of σ^2, i know how to do it for σ, to obtain
    1/x(bar), was wondering how to obtain for σ^2, i guess you just dont square bot sides. It should tale the form of kƩ(x_i)^2.
    many thanks any help would be much appreciated.
     
  2. jcsd
  3. Dec 23, 2011 #2

    mathman

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    Try to clarify what you are doing. Usually estimations are made for σ2 and σ is just the square root.
     
  4. Dec 23, 2011 #3
    Note, the rate parameter estimate is [itex]\hat \lambda = 1/\bar x[/itex]. The mean is therefore [itex]1/\lambda [/itex] and the variance is [itex]1/\lambda^2[/itex]. The standard deviation is not really defined for the exponential distribution because it is not symmetrical around the mean. The usual maximum likelihood estimate of the mean [itex]\bar x = (\sum_{i=1}^{i=n} x_i)/n[/itex] is unbiased, and therefore so is the estimate of lambda.
     
    Last edited: Dec 24, 2011
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