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Lukacs's proportion-sum independence theorem : ウィキペディア英語版 | Lukacs's proportion-sum independence theorem In statistics, Lukacs's proportion-sum independence theorem is a result that is used when studying proportions, in particular the Dirichlet distribution. It is named for Eugene Lukacs. ==The theorem == If ''Y''1 and ''Y''2 are non-degenerate, independent random variables, then the random variables : are independently distributed if and only if both ''Y''1 and ''Y''2 have gamma distributions with the same scale parameter.
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