What statistical model have such $\theta = \sqrt{\frac{\sum\limits_{i = 1}^{n} x_i}{2n}}$ estimation for parameter?

Question

What statistical model have such estimation for parameter? Model have only one parameter.

$$\theta = \sqrt{\frac{\sum\limits_{i = 1}^{n} x_i}{2n}}$$

I've tried to build model from exponetial family. But it seems that this model should be not from exponetial family.

Could you guess statistical model?