Statistics Graduate Level Quiz
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STATISTICAL INFERENCE
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Suppose X1,…,XnX_1,\ldots,X_n are independent gamma random variables with density f(x∣α,β)=βαxα−1e−βx/Γ(α)f(x\mid\alpha,\beta)=\beta^\alpha x^{\alpha-1}e^{-\beta x}/\Gamma(\alpha) for x>0x>0, where both α\alpha and β\beta are unknown. Which statistic is jointly sufficient for (α,β)\left(\alpha,\beta\right)?
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