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