Question

The method of moment estimator of parameter '$\alpha$' in the following probability density function $f_{X}(x)=\begin{cases}\frac{\alpha}{x^{\alpha+1}}, & x>1, \alpha>1 \\0 & \text{otherwise}\end{cases}$ is

• A. $\frac{1}{\overline{x}-1}$
• B. $\frac{\overline{x}}{\overline{x}-1}$
• C. $\frac{\overline{x}-1}{\overline{x}}$
• D. $\overline{x}-1$

Hint:

For Pareto-like distributions, the mean is $\frac{\alpha}{\alpha-1}$. If the mean is $\mu$, then $\alpha = \frac{\mu}{\mu-1}$. Just replace $\mu$ with the sample mean $\overline{x}$ to get the MoM estimator instantly.

Answer 1

The Correct Option is B