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.

F Distribution

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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