11. Both definitions are special cases of the scaled-inverse-chi-squared distribution . 12. It follows the chi-squared distribution . 13. The noncentral chi-squared distribution generalizes this to normal distributions with arbitrary mean and variance. 14. For number of dimensions other than 2, the cumulative chi-squared distribution should be consulted. 15. The resulting value can be compared to the chi-squared distribution to determine the goodness of fit. 16. The chi square distribution for " k " degrees of freedom will then be given by: 17. It can therefore be regarded as a generalized chi-squared distribution for even numbers of degrees of freedom. 18. Under the null hypothesis, it has approximately a chi-squared distribution whose number of degrees of freedom are 19. Other Bayesians prefer to parametrize the inverse gamma distribution differently, as a scaled inverse chi-squared distribution . 20. So wherever a normal distribution could be used for a hypothesis test, a chi-squared distribution could be used.
