The Snedecor’s \(F\)-distribution or the Fisher-Snedecor distribution (after Sir Ronald A. Fisher and George W. Snedecor) or short the \(F\)-distribution is a continuous probability distribution with range \([0, +\infty)\), depending on two parameters denoted \(v_1, v_2\) (Lovric 2011). In statistical applications, \(v_1, v_2\) are positive integers.

Let \(Y_1\) and \(Y_2\) be two independent random variables distributed as chi-square, with \(v_1\) and \(v_2\) degrees of freedom, respectively. Then the distribution of the ratio (\(Z\))

\[Z = \frac{Y_1/v_1}{Y_2/v_2}\]

is called the \(F\)-distribution with \(v_1\) and \(v_2\) degrees of freedom. The \(F\)-distribution is often referred to as the distribution of the variance ratio (Lovric 2011).

A \(F\)-distribution has two numbers of degrees of freedom, \(v_1\) and \(v_2\), determining its shape. The first number of degrees of freedom, \(v_1\), is called the degrees of freedom of the numerator and the second, \(v_2\), the degrees of freedom of the denominator.

Basic Properties of \(F\)-Curves (Weiss 2010)

• The total area under an \(F\)-curve equals 1.
  
• An \(F\)-curve starts at 0 on the horizontal axis and extends indefinitely to the right, approaching, but never touching, the horizontal axis as it does so.
• An \(F\)-curve is right skewed.

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