# Sufficient Statistic of Uniform $(-\theta,0)$

by Pedros   Last Updated July 12, 2019 06:19 AM

Let $$X_1, ... , X_n$$ be i.i.d random variables Uniform $$(-\theta,0)$$ , with $$\theta > 0$$ parameter

\begin{align}f_{\theta}(x_1,x_2,\cdots,x_n)&=\prod_{i=1}^nf(x_i;\theta) \\&=\frac{1}{(\theta)^n}\mathbf1_{-\theta

So can we conclude that the sufficient statistic for $$-\theta$$ so for $$\theta$$ too is $$X_{(1)}$$.

Also that the sufficient statistic for $$\theta$$ is $$-X_{(1)}$$. ??

Thus, both $$X_{(1)}$$ and $$-X_{(1)}$$ are sufficient statistics for $$\theta$$ ?

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