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Pareto Distribution Mean and Variance Calculator

μ = α·x_m / (α−1) for α > 1; σ² = x_m²·α / ((α−1)²(α−2)) for α > 2.

Compute the mean and variance of a Pareto(x_m, α) distribution. The mean is finite only for α > 1, the variance only for α > 2; otherwise the moment is infinite and reported as 0 (with a flag).

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

μ = α·x_m / (α−1) (α > 1); σ² = x_m²·α / ((α−1)²(α−2)) (α > 2).

In depth

Compute the mean and variance of a Pareto(x_m, α) distribution. The mean is finite only for α > 1, the variance only for α > 2; otherwise the moment is infinite and reported as 0 (with a flag).