F-distribution

{{Probability distribution | name = Fisher–Snedecor | type = density | pdf_image = 325px| | cdf_image = 325px| | parameters = d1, d2 > 0 deg. of freedom | support = x \in (0, +\infty)\; if d_1 = 1, otherwise x \in [0, +\infty)\; | pdf = \frac{\sqrt{\frac{(d_1 x)^{d_1} d_2^{d_2}}{(d_1 x+d_2)^{d_1+d_2}}}}{x\,\mathrm{B}\!\left(\frac{d_1}{2},\frac{d_2}{2}\right)}\! | cdf = I_{\frac{d_1 x}{d_1 x + d_2}} \left(\tfrac{d_1}{2}, \tfrac{d_2}{2} \right) | mean = \frac{d_2}{d_2-2}\! for d2 > 2 | median = | mode = \frac{d_1-2}{d_1}\;\frac{d_2}{d_2+2} for d1 > 2 | variance = \frac{2\,d_2^2\,(d_1+d_2-2)}{d_1 (d_2-2)^2 (d_2-4)}\! for d2 > 4 | skewness = \frac{(2 d_1 + d_2 - 2) \sqrt{8 (d_2-4)}}{(d_2-6) \sqrt{d_1 (d_1 + d_2 -2)}}\!for d2 > 6 | kurtosis = see text | entropy = \begin{align} & \ln \Gamma{\left(\tfrac{d_1}{2} \right)} + \ln \Gamma{\left(\tfrac{d_2}{2} \right)} - \ln \Gamma{\left(\tfrac{d_1+d_2}{2} \right)} \\ &+ \left(1-\tfrac{d_1}{2} \right) \psi{\left(1+\tfrac{d_1}{2} \right)} - \left(1+\tfrac{d_2}{2} \right) \psi{\left(1+\tfrac{d_2}{2} \right)} \\ &+ \left(\tfrac{d_1 + d_2}{2} \right) \psi{\left(\tfrac{d_1 + d_2}{2} \right)} + \ln \frac{d_2}{d_1} \end{align} | mgf = does not exist, raw moments defined in text and in | char = see text }}

In probability theory and statistics, the '''F-distribution or F-ratio, also known as Snedecor's F distribution or the Fisher–Snedecor distribution' (after Ronald Fisher and George W. Snedecor), is a continuous probability distribution that arises frequently as the null distribution of a test statistic, most notably in the analysis of variance (ANOVA) and other F-tests.