Chi-squared stochastic ordering
= Chi-squared stochastic ordering
If $r<s$, coupling by extra independent squared normals gives $\chi_s^2=\chi_r^2+W$ with $W\geq0$, so every fixed upper quantile increases with the degrees of freedom.
= Chi-squared stochastic ordering
If $r<s$, coupling by extra independent squared normals gives $\chi_s^2=\chi_r^2+W$ with $W\geq0$, so every fixed upper quantile increases with the degrees of freedom.