Inverse Gamma Distribution Variance Calculator
For an Inverse Gamma distribution with shape parameter \( \alpha \) and scale parameter \( \beta \), the variance is given by: $$ \text{Variance} = \frac{\beta^2}{(\alpha-1)^2(\alpha-2)}, \quad \text{for } \alpha > 2. $$
* Enter \( \alpha \) (must be \(>0\)) and \( \beta \) (must be \(>0\)). Note: The variance is defined only if \(\alpha > 2\).
Step 1: Enter Parameters
e.g., 3 (must be > 2 for variance to be defined)
e.g., 4
How It Works
The Inverse Gamma distribution is defined by the probability density function:
$$ f(x;\alpha,\beta)=\frac{\beta^\alpha}{\Gamma(\alpha)}\,x^{-\alpha-1}e^{-\beta/x},\quad x>0. $$
The variance of this distribution is given by:
$$ \text{Variance} = \frac{\beta^2}{(\alpha-1)^2(\alpha-2)} \quad \text{for } \alpha > 2. $$
If \(\alpha \le 2\), the variance is undefined (or infinite).
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