# Using Method of Moments to find estimator [closed]

$$\large fx(x;a)=\frac{a}{x^{a+1}} , x \gt 1$$

where $$a \gt1$$ is the parameter of the distribution.

Find the estimator for $$a$$ using the method of moments.

## closed as off-topic by Siong Thye Goh, StubbornAtom, Ernie060, Lee David Chung Lin, ShaileshMay 11 at 3:08

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The mean is $$\Bbb E X=\int_1^\infty ax^{-a}dx=\frac{a}{a-1}$$. Given an empirical estimator $$\hat{\mu}$$ of this mean, MOM's estimator $$\hat{a}$$ of $$a$$ satisfies $$\hat{\mu}=\frac{\hat{a}}{\hat{a}-1}\implies\hat{a}=\frac{\hat{\mu}}{\hat{\mu}-1}.$$