finv

F inverse cumulative distribution function

Syntax

X = finv(P,V1,V2)


Description

X = finv(P,V1,V2) computes the inverse of the F cdf with numerator degrees of freedom V1 and denominator degrees of freedom V2 for the corresponding probabilities in P. P, 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 P must lie on the interval [0 1].

The F inverse function is defined in terms of the F cdf as

$$x=F^{-1}\left(p|{\nu }_1,{\nu }_2\right)=\left\{x:F\left(x|{\nu }_1,{\nu }_2\right)=p\right\}$$

where

$$p=F(x|{\nu }_1,{\nu }_2)={\displaystyle \underset{0}{\overset{x}{\int }}\frac{\Gamma \left[\frac{({\nu }_1+{\nu }_2)}{2}\right]}{\Gamma \left(\frac{{\nu }_1}{2}\right)\Gamma \left(\frac{{\nu }_2}{2}\right)}}{\left(\frac{{\nu }_1}{{\nu }_2}\right)}^{\frac{{\nu }_1}{2}}\frac{t^{\frac{{\nu }_1-2}{2}}}{{\left[1+\left(\frac{{\nu }_1}{{\nu }_2}\right)t\right]}^{\frac{{\nu }_1+{\nu }_2}{2}}}dt$$

Examples

Find a value that should exceed 95% of the samples from an F distribution with 5 degrees of freedom in the numerator and 10 degrees of freedom in the denominator.

x = finv(0.95,5,10)
x =
  3.3258

You would observe values greater than 3.3258 only 5% of the time by chance.

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).