Rozkład F Snedecora

Rozkład F Snedecora
Gęstość prawdopodobieństwa
Dystrybuanta (c) Pdbailey, CC-BY-SA-3.0
Parametry	${\displaystyle d_{1}>0,\ d_{2}>0}$ stopni swobody
Nośnik	${\displaystyle x\in [0;+\infty )}$
Gęstość prawdopodobieństwa	${\displaystyle {\frac {\sqrt {\frac {(d_{1}\,x)^{d_{1}}\,\,d_{2}^{d_{2}}}{(d_{1}\,x+d_{2})^{d_{1}+d_{2}}}}}{x\,\mathrm {B} \!\left({\frac {d_{1}}{2}},{\frac {d_{2}}{2}}\right)}}}$
Dystrybuanta	${\displaystyle I_{\frac {d_{1}x}{d_{1}x+d_{2}}}(d_{1}/2,d_{2}/2)}$
Wartość oczekiwana (średnia)	${\displaystyle {\frac {d_{2}}{d_{2}-2}}}$ ${\displaystyle {\text{ dla }}d_{2}>2}$
Moda	${\displaystyle {\frac {d_{1}-2}{d_{1}}}\;{\frac {d_{2}}{d_{2}+2}}}$ ${\displaystyle {\text{ dla }}d_{1}>2}$
Wariancja	${\displaystyle {\frac {2\,d_{2}^{2}\,(d_{1}+d_{2}-2)}{d_{1}(d_{2}-2)^{2}(d_{2}-4)}}}$ ${\displaystyle {\text{ dla }}d_{2}>4}$
Współczynnik skośności	${\displaystyle {\frac {(2d_{1}+d_{2}-2){\sqrt {8(d_{2}-4)}}}{(d_{2}-6){\sqrt {d_{1}(d_{1}+d_{2}-2)}}}}}$ for ${\displaystyle d_{2}>6}$
Kurtoza	${\displaystyle {\tfrac {12(20d_{2}-8d_{2}^{2}+d_{2}^{3}+44d_{1}-32d_{1}d_{2}}{d_{1}(d_{2}-6)(d_{2}-8)(d_{1}+d_{2}-2)}}+}$ ${\displaystyle +{\tfrac {5d_{2}^{2}d_{1}-22d_{1}^{2}+5d_{2}d_{1}^{2}-16)}{d_{1}(d_{2}-6)(d_{2}-8)(d_{1}+d_{2}-2)}}.}$
Odkrywca	Ronald Fisher, George W. Snedecor

Rozkład F Snedecora – rozkład prawdopodobieństwa zmiennej losowej F o d₁, d₂ stopniach swobody.

Jeżeli X i Y są niezależne oraz ${\displaystyle X\sim \chi ^{2}(d_{1})\ {}}$ i ${\displaystyle {}\ Y\sim \chi ^{2}(d_{2}),}$ to:

${\displaystyle {\frac {X/d_{1}}{Y/d_{2}}}\sim F(d_{1},d_{2}).}$

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