Manuals/calci/FDIST

FDIST (Number,DegreeOfFreedom1,DegreeOfFreedom2)

$Number$ is the value of the function
and are numbers of degrees of freedom.
- Returns the F probability distribution

Description

This function gives the value of F probability distribution.
This distribution is continuous probability distribution and it is called Fisher-Snedecor distribution.
The F distribution is an asymmetric distribution that has a minimum value of 0, but no maximum value.
In $FDIST(Number,DegreeOfFreedom1,DegreeOfFreedom2),Number$ is the value of the function , $DegreeOfFreedom1$ is the numerator degrees of freedom and $DegreeOfFreedom2$ is the denominator degrees of freedom.
This distribution is the ratio of two chi-square distributions with degrees of freedom r1 and r2, respectively, where each chi-square has first been divided by its degrees of freedom.
The Probability density function of the F distribution is:

$f(x,r_{1},r_{2})={\frac {\Gamma [{\frac {r_{1}+r_{2}}{2}}]({\frac {r_{1}}{r_{2}}})^{\tfrac {r_{1}}{2}}}{\Gamma ({\frac {r_{1}}{2}})\Gamma ({\frac {r_{2}}{2}})}}*{\frac {(x)^{{\tfrac {r_{1}}{2}}-1}}{({\frac {1+r_{1}x}{r_{2}}})^{\tfrac {r_{1}+r_{2}}{2}}}}$ $0<x<\infty$ where $\Gamma$ is the Gamma Function.

The gamma function is defined by $\Gamma (t)=\int \limits _{0}^{\infty }x^{t-1}e^{-x}dx$ .

When the value of DegreeOfFreedom1 and DegreeOfFreedom2 are not integers ,then it is converted in to integers.

This function will give the result as error when

 1. any one of the argument is non-numeric.
 2. Number is negative
 3. If DegreeOfFreedom1<1  or DegreeOfFreedom2> $10^{10}$  and  DegreeOfFreedom2<1 or DegreeOfFreedom2>  $10^{10}$