Inverse Gamma Distribution Mode Calculator
For an Inverse Gamma distribution with shape parameter \( \alpha \) and scale parameter \( \beta \), the mode is given by: $$ \text{Mode} = \frac{\beta}{\alpha+1}. $$
* Enter \( \alpha \) (must be \(>0\)) and \( \beta \) (must be \(>0\)).
Step 1: Enter Parameters
e.g., 2
e.g., 3
How It Works
The Inverse Gamma distribution is defined by the PDF: $$ f(x;\alpha,\beta)=\frac{\beta^\alpha}{\Gamma(\alpha)}\,x^{-\alpha-1}e^{-\beta/x},\quad x>0. $$
To find the mode, we differentiate the log of the PDF with respect to \(x\) and set the derivative equal to zero.
This yields the formula: $$ \text{Mode} = \frac{\beta}{\alpha+1}. $$
Simply enter the parameters \(\alpha\) and \(\beta\) to compute the mode.
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