Let Y 1 ,Y 2 ,...,Y n be a random sample from a Pareto pdf, f Y (y; ) = /(1 + y) +1 ,

Let Y₁,Y₂,...,Y_n be a random sample from a Pareto pdf, f_Y (y; θ) = θ/(1 + y) ^θ+1 , 0 ≤ y ≤ ∞; 0 Y (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.

gw (w; 0) = eK(w)p(0)+S(w)+q(0)