Let Y 1 ,Y 2 ,...,Y n be a random sample from a Pareto pdf, f Y

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Let Y1,Y2,...,Yn be a random sample from a Pareto pdf, fY (y; θ) = θ/(1 + y) θ+1 , 0 ≤ y ≤ ∞; 0 < θ < ∞. Write fY (y; θ) in exponential form and deduce a sufficient statistic for θ (see Question 5.6.9).


Data in Question 5.6.9

A pdf gW (w; θ) is said to be expressed in exponential form if it can be written as 

where the range of W is independent of θ. Show that  is sufficient for θ.

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