- Noncentral F Distribution

Let χ2m(δ) be a noncentral chi-square random variable with degrees of freedom (df) = m, and noncentrality parameter δ, and χ2n be a chi-square random variable with df = n. If χ2m(δ) and χ

2 n are independent, then the distribution of the ratio

Fm,n(δ) = χ2m(δ)/m

χ2n/n

is called the noncentral F distribution with the numerator df = m, the denominator df = n, and the noncentrality parameter δ.