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The F distribution (Snedecor”s F distribution or the FisherSnedecor distribution) represents continuous probability distribution which occurs frequently as null distribution of test statistics. It happens mostly during analysis of variance or F-test.
Probability density function
Probability density function of F distribution is given as:
Formula
${ f(x; d_1, d_2) = frac{sqrt{frac{(d_1 x)^{d_1} d_2^{d_2}}{(d_1x+d_2)^{d_1+d_2}}}}{x beta (frac{d_1}{2}, frac{d_2}{2})} }$
Where −
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${d_1}$ = positive parameter.
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${d_2}$ = positive parameter.
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${x}$ = random variable.
Cumulative distribution function
Cumulative distribution function of F distribution is given as:
Formula
${ F(x; d_1, d_2) = I_{frac{d_1x}{d_1x+d_2}}(frac{d_1}{2}, frac{d_2}{2})}$
Where −
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${d_1}$ = positive parameter.
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${d_2}$ = positive parameter.
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${x}$ = random variable.
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${I} $ = lower incomplete beta function.
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