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Competitive Stats
Q28Section I (Objective (Q1–Q80))28 of 80

Sufficient statistic — power distribution

Let x1,x2,…,xnx_1,x_2,\dots,x_n be a random sample from a distribution with p.d.f.

f(x)={θxθ−1;0<x<1,0<θ<∞0;otherwise.f(x)=\begin{cases}\theta x^{\theta-1}; & 0<x<1, 0<\theta<\infty\\ 0; & \text{otherwise.}\end{cases}

Then a sufficient statistic for θ\theta is:

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