Manuals/calci/FDIST

FDIST (Number,DegreeOfFreedom1,DegreeOfFreedom2)

• $Number$ is the value of the function
• $DegreeOfFreedom1$ and $DegreeOfFreedom2$ are numbers of degrees of freedom.

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> $10^{10}$

ZOS

• The syntax is to find FDIST in ZOS is $FDIST(Number,DegreeOfFreedom1,DegreeOfFreedom2)$.
  • $Number$ is the value of the function.
• For e.g.,FDIST(85.2,22,18)
• FDIST(67..70,6,8)

Examples

1. =FDIST(20.6587,7,3) = 0.01526530981
2. =FDIST(70.120045,12.2,6.35) = 0.000011229898
3. =FDIST(10,1.3,1.5) = 0.134947329626
4. =FDIST(-28,4,6) = NAN

Related Videos

F Distribution

See Also

• FINV
• FTEST

References

F-Distribution

• List of Main Z Functions

• Z3 home