Pareto Distribution Mean Calculator

Enter the scale parameter $ x_m $ and the shape parameter $\alpha$ to calculate the mean of the Pareto distribution.

* Note: The mean exists only if $\alpha > 1$. For $\alpha \le 1$, the mean is undefined (infinite).

Step 1: Enter Parameters

Scale Parameter, $ x_m $:

e.g., 1

Shape Parameter, $\alpha$:

e.g., 2 (must be greater than 1 for the mean to exist)

The mean of the Pareto distribution is given by: $$ \mu = \frac{\alpha x_m}{\alpha – 1} \quad \text{for } \alpha > 1. $$

If $\alpha \le 1$, the mean is undefined (infinite).

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