Inverse Gamma Distribution Sample Generator
Generate random samples from an Inverse Gamma distribution.
* Enter the shape parameter \(\alpha>0\), scale parameter \(\beta>0\), and the number of samples.
Step 1: Enter Parameters
e.g., 2
e.g., 3
e.g., 10
How It Works
The Inverse Gamma distribution is defined by the PDF: $$ f(y;\alpha,\beta)=\frac{\beta^\alpha}{\Gamma(\alpha)}\,y^{-\alpha-1}e^{-\beta/y},\quad y>0. $$
A useful relationship is that if $$ X \sim \text{Gamma}\left(\alpha,\, \text{scale}=\frac{1}{\beta}\right), $$ then $$ Y = \frac{1}{X} \sim \text{Inverse Gamma}(\alpha,\beta). $$
This calculator generates Gamma random variables using the Marsaglia and Tsang method (with a transformation if \(\alpha < 1\)), and then outputs their reciprocals to produce Inverse Gamma samples.
Related Calculators
- Inverse Gamma Distribution Variance Calculator: Quickly determine the variance of an Inverse Gamma distribution for α > 2.
- Inverse Gamma Distribution Mode Calculator: Compute the mode to identify the most frequently occurring value.
- Inverse Gamma Distribution Mean Calculator: Instantly calculate the mean (average) for α > 1.
- Inverse Gamma Distribution Inverse CDF Calculator: Calculate cumulative probabilities precisely at specific distribution points.
- Inverse Gamma Distribution PDF Calculator: