Pareto Distribution Variance Calculator

Pareto Distribution Variance Calculator

Enter the scale parameter \( x_m \) and the shape parameter \(\alpha\) to calculate the variance of the Pareto distribution.

* Note: The variance exists only if \(\alpha > 2\). For \(\alpha \le 2\), the variance is undefined (infinite).

Step 1: Enter Parameters

e.g., 1

e.g., 3 (must be greater than 2 for the variance to exist)

How It Works

The variance of the Pareto distribution is given by: $$ \text{Var}(X) = \frac{x_m^2 \, \alpha}{(\alpha – 1)^2 (\alpha – 2)} \quad \text{for } \alpha > 2. $$

If \(\alpha \le 2\), the variance is undefined (infinite).

Formula: \( \text{Var}(X) = \frac{x_m^2 \, \alpha}{(\alpha – 1)^2 (\alpha – 2)} \) (for \(\alpha > 2\))

Related Calculators