# 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 Inf]`.

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```

## Extended Capabilities

### Topics

Introduced before R2006a