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Suppose you want to estimate the parameters $\alpha$ and $\beta$ of a $\text{gamma}(\alpha, \beta)$ distribution where we know that $\alpha = \beta$. Would you treat this as a distribution with one or two unknown parameters? It seems that you can treat it as a distribution with 1 unknown parameter.

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    You could do that produce an estimator, but it would not be$a$sufficient statistics and so cannot be optimal.2012-04-07

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