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Math Help - Exponential Family & Sufficient Statistic.

  1. #1
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    Exponential Family & Sufficient Statistic.

    The power family of distributions have densities

    f(x;\alpha,\theta) = \frac{\alpha x^{\alpha -1}}{\theta^{\alpha}}, 0 \leq x \leq \theta. 0 elsewhere.

    If \theta is known, show hat f(x;\alpha) is in the exponential family and find a sufficient statistic for \alpha.
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  2. #2
    MHF Contributor matheagle's Avatar
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    suff for \alpha is \Pi_{i=1}^n X_i

    and suff for \theta is the largest X_i

    both via the factorization theorem.
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  3. #3
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    Thank you, do you convert the pdf into the form of the exponential families to show? Then extract the term which is dependent on theta to determine the sufficient statistic?
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