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

$$y=f(x|{\nu }_1,{\nu }_2)=\frac{\Gamma \left[\frac{({\nu }_1+{\nu }_2)}{2}\right]}{\Gamma \left(\frac{{\nu }_1}{2}\right)\Gamma \left(\frac{{\nu }_2}{2}\right)}{\left(\frac{{\nu }_1}{{\nu }_2}\right)}^{\frac{{\nu }_1}{2}}\frac{x^{\frac{{\nu }_1-2}{2}}}{{\left[1+\left(\frac{{\nu }_1}{{\nu }_2}\right)x\right]}^{\frac{{\nu }_1+{\nu }_2}{2}}}$$

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

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced before R2006a