# Statistics F distribution – lesscss

By | September 29, 2019

# Statistics – F distribution

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 −

• \${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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