ABSTRACT
Let X and Y be independent chi-square random variables with degrees of freedoms (dfs) m and n, respectively. The distribution of the ratio
Fm,n = (X m )
(Y n )
is called the F distribution with the numerator df = m and the denominator df = n. The probability density function of an Fm,n distribution is given by
f(x|m,n) = Γ ( m+n 2
) Γ ( m 2
) Γ ( n 2
)m/2 [ 1 + mx
]m/2+n/2 , m > 0, n > 0, x > 0. Let S2i denote the variance of a random sample of size ni from a N(µi, σ
2) distribution, i = 1, 2. Then the variance ratio
distribution. For this reason, the F distribution is also known as the variance ratio distribution.
