Inverse Gamma Distribution Sample Generator

Generate random samples from an Inverse Gamma distribution.

* Enter the shape parameter $α > 0$ , scale parameter $β > 0$ , and the number of samples.

Step 1: Enter Parameters

Shape Parameter,

α

e.g., 2

Scale Parameter,

β

e.g., 3

Number of Samples:

e.g., 10

How It Works

The Inverse Gamma distribution is defined by the PDF: $f (y; α, β) = \frac{β^{α}}{Γ (α)} y^{- α - 1} e^{- β / y}, y > 0.$

A useful relationship is that if $X \sim Gamma (α, scale = \frac{1}{β}),$ then $Y = \frac{1}{X} \sim Inverse Gamma (α, β) .$

This calculator generates Gamma random variables using the Marsaglia and Tsang method (with a transformation if $α < 1$ ), 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:

Step 1: Enter Parameters

Generated Samples

How It Works

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