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;d1,d2)=(d1x)d1dd22(d1x+d2)d1+d2√xβ(d12,d22)f(x;d1,d2)=(d1x)d1d2d2(d1x+d2)d1+d2xβ(d12,d22)

Where −

·        d1d1 = positive parameter.

·        d2d2 = positive parameter.

·        xx = random variable.

Cumulative distribution function

Cumulative distribution function of F distribution is given as:

Formula

F(x;d1,d2)=Id1xd1x+d2(d12,d22)F(x;d1,d2)=Id1xd1x+d2(d12,d22)

Where −

·        d1d1 = positive parameter.

·        d2d2 = positive parameter.

·        xx = random variable.

·        II = lower incomplete beta function.