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Math Help - expectation of 1-(1/xbar)

  1. #1
    Junior Member
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    expectation of 1-(1/xbar)

    Hi, could you please help with this. I'm tring to find out whether the estimator
    1-(1/xbar) for lambda is biased. Thank-you.

    If we have a random sample X1,....,.Xn from a pareto distribution with pdf

    f(x;lambda)= (1/lambda)x^(-(1+1/lambda))

    then what is E[1-(1/xbar)]?

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  2. #2
    MHF Contributor matheagle's Avatar
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    I guess the support is (1,\infty)

    I don't think there is a nice MGf here.
    We need the density of the sum of paretos.
    dividing that by n and the rest would be easy.
    But we would need to figure out the density of a sum of n iid paretos.

    If you try to obtain the MGF and ley Y=X-1 you can almost make it a gamma density
    So please state your complete density.
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