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

1 Answer
Dec 8, 2017

Answer:

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