Inverse Chi-Squared Calculator

Formula

To calculate the Inverse Chi-Squared (X²):

$X² = \frac{df}{χ²}$

Where:

$X²$ is the Inverse Chi-Squared value
$df$ is the degrees of freedom
$χ²$ is the chi-squared value

What is Inverse Chi-Squared?

The inverse chi-squared distribution is a continuous probability distribution that is often used in Bayesian statistics. It is the distribution of the reciprocal of a variable that has a chi-squared distribution. This distribution is particularly useful in the context of Bayesian inference, where it is used as a prior distribution for the variance of a normal distribution. The inverse chi-squared distribution is parameterized by the degrees of freedom, which determines the shape of the distribution.

Example Calculation

Let's assume the following values:

Degrees of Freedom $df$ = 10
Chi-Squared Value $χ²$ = 5

Step 1: Divide the degrees of freedom by the chi-squared value:

$X² = \frac{df}{χ²} = \frac{10}{5} = 2$

The Inverse Chi-Squared value is 2.