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 \(\alpha > 1\).
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