Inverse Gamma Distribution Mean Calculator

Inverse Gamma Distribution Mean Calculator

For an Inverse Gamma distribution with shape parameter \( \alpha \) and scale parameter \( \beta \), the mean is given by: $$ \text{Mean} = \frac{\beta}{\alpha-1}, \quad \text{for } \alpha > 1. $$

* Enter \( \alpha \) (must be \( > 0 \)) and \( \beta \) (must be \( > 0 \)). Note: The mean is only defined for \( \alpha > 1 \).

Step 1: Enter Parameters

e.g., 2 (mean is defined only if \(\alpha > 1\))

e.g., 3

How It Works

The mean of an Inverse Gamma distribution is defined as:

$$ \text{Mean} = \frac{\beta}{\alpha-1}, \quad \text{for } \alpha > 1. $$

If \(\alpha \le 1\), the mean is undefined (or infinite). This calculator only returns a valid result when \(\alpha > 1\).

Formula: \( \text{Mean} = \frac{\beta}{\alpha-1} \) (valid for \(\alpha > 1\))

Related Calculators