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- Statistics - Discussion
Statistics - F distribution
The F distribution (Snedecor's F distribution or the Fisher–Snedecor 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 −
${d_1}$ = 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.
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