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If we have two random variables Y1 and Y2 having chi-square distribution with a and b degrees of freedom respectively, ratio

will have F-distribution with a and b degrees of freedom. This distribution is also known as Fisher distribution.
On the right, you can see the probability density function of the F-distribution for some a's and b's. Its analytical form is:

Cumulative distribution function of the F-distribution is:
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This module contains algorithms of calculation of the cumulative distribution function (FDistribution subroutine), its own complement (FCDistribution subroutine) and its inverse function (InvFDistribution subroutine).
This article is intended for personal use only.
C# source.
C++ source.
C++ source. MPFR/GMP is used.
GMP source is available from gmplib.org. MPFR source is available from www.mpfr.org.
FreePascal version.
Delphi version.
VB.NET version.
VBA version.
Python version (CPython and IronPython are supported).
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ALGLIB® - numerical analysis library, 1999-2012. |