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fpdf

F probability density function

Syntax

Y = fpdf(X,V1,V2)

Description

Y = fpdf(X,V1,V2) computes the F pdf at each of the values in X using the corresponding numerator degrees of freedom V1 and denominator degrees of freedom V2. X, V1, and V2 can be vectors, matrices, or multidimensional arrays that all have the same size. A scalar input is expanded to a constant array with the same dimensions as the other inputs. V1 and V2 parameters must contain real positive values, and the values in X must lie on the interval [0 ∞).

The probability density function for the F distribution is

$y=f\left(x|{\nu }_{1},{\nu }_{2}\right)=\frac{\Gamma \left[\frac{\left({\nu }_{1}+{\nu }_{2}\right)}{2}\right]}{\Gamma \left(\frac{{\nu }_{1}}{2}\right)\Gamma \left(\frac{{\nu }_{2}}{2}\right)}{\left(\frac{{\nu }_{1}}{{\nu }_{2}}\right)}^{\frac{{\nu }_{1}}{2}}\frac{{x}^{\frac{{\nu }_{1}-2}{2}}}{{\left[1+\left(\frac{{\nu }_{1}}{{\nu }_{2}}\right)x\right]}^{\frac{{\nu }_{1}+{\nu }_{2}}{2}}}$

Examples

y = fpdf(1:6,2,2)
y =
0.2500  0.1111  0.0625  0.0400  0.0278  0.0204

z = fpdf(3,5:10,5:10)
z =
0.0689  0.0659  0.0620  0.0577  0.0532  0.0487