Mathematics · Mathematical Statistics

Suppose that (X 1 , Y 1 ), (X 2 , Y 2 ), ..., (X n , Y n ) are independent and identically distributed random variables having a uniform distribution on the triangle with vertices (0, 0), (θ, 0), and (0, θ), where θ > 0. A sufficient statistic for θ is:

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max 1≤i≤n (X i + Y i )

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Suppose that (X 1 , Y 1 ), (X 2 , Y 2 ), ..., (X n , Y n ) are independent and identically distributed random variables having a uniform distribution on the triangle with vertices (0, 0), (&theta;, 0), and (0, &theta;), where &theta; > 0. A sufficient statistic for &theta; is: