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A two-parameter family of univariate distributions defined on the interval $[0,1]$.

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Statistical model with $\Gamma(\alpha_i,1)$ sample

We are given statistical sample of $X=(X_1,X_2,X_3)$, where $X_i\sim\Gamma(\alpha_i,1)$ and independent. Let $Z=X_1+X_2+X_3$ and $T$ three dimensional statistic $T:=(\frac{X_1}{Z},\frac{X_2}{Z},\frac{ …
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