Question

What can a chi-squared distribution be used to describe?

Answer 1

Chi Squared distributions can be used to describe statistical quantities which are a function of a sum of squares.

Explanation:

The Chi Squared distribution is the distribution of a value which is the sum of squares of `k` normally distributed random variables.

`Q=sum_(i=1)^k Z_i^2`

The PDF of the Chi Squared distribution is given by:

`f(x;k)=1/(2^(k/2)Gamma(k/2)) x^(k/2-1)e^(-x/2)`

Where `k` is the number of degrees of freedom, and `x` is the value of `Q` for which we seek the probability.

The usefulness of the Chi Squared distribution is in modelling things which involve the sums of squared values. Two specific examples are:

• Analysis of Variance tests (variance is a sum of squared values)
• Goodness of fit (for a least squares fit where the error is a sum of squared values)

Taken from:
https://en.wikipedia.org/wiki/Chi-squared_distribution