Fratio (or F) Distribution¶
Defined for x>0 . The distribution of (X1/X2)(ν2/ν1) if X1 is chi-squared with v1 degrees of freedom and X2 is chi-squared with v2 degrees of freedom.
f(x;ν1,ν2)=νν2/22νν1/21xν1/2−1(ν2+ν1x)(ν1+ν2)/2B(ν12,ν22)F(x;v1,v2)=I(ν12,ν22,ν2xν2+ν1x)G(q;ν1,ν2)=[ν2I−1(ν1/2,ν2/2,q)−ν1ν2]−1.
μ=ν2ν2−2ν2>2μ2=2ν22(ν1+ν2−2)ν1(ν2−2)2(ν2−4)v2>4γ1=2(2ν1+ν2−2)ν2−6√2(ν2−4)ν1(ν1+ν2−2)ν2>6γ2=3[8+(ν2−6)γ21]2ν−16ν2>8
Implementation: scipy.stats.f