# Difference between revisions of "Manuals/calci/FDIST"

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− | <div style="font-size:30px">'''FDIST( | + | <div style="font-size:30px">'''FDIST (Number,DegreeOfFreedom1,DegreeOfFreedom2)'''</div><br/> |

− | *<math> | + | *<math>Number</math> is the value of the function |

− | *<math> | + | *<math>DegreeOfFreedom1</math> and <math>DegreeOfFreedom2</math> are numbers of degrees of freedom. |

+ | **FDIST(), returns the F probability distribution. | ||

==Description== | ==Description== | ||

Line 7: | Line 8: | ||

*This distribution is continuous probability distribution and it is called Fisher-Snedecor 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. | *The F distribution is an asymmetric distribution that has a minimum value of 0, but no maximum value. | ||

− | *In <math>FDIST( | + | *In <math>FDIST (Number,DegreeOfFreedom1,DegreeOfFreedom2), Number </math> is the value of the function ,<math>DegreeOfFreedom1</math> is the numerator degrees of freedom and <math>DegreeOfFreedom2</math> 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. | *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: | *The Probability density function of the F distribution is: | ||

<math>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_1x}{r_2})^{\tfrac{r_1+r_2}{2}}}</math> | <math>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_1x}{r_2})^{\tfrac{r_1+r_2}{2}}}</math> | ||

− | 0<x<\infty</math> where | + | <math>0<x<\infty</math> where <math>\Gamma</math> is the Gamma Function. |

− | *The gamma function is defined by Gamma(t) = | + | *The gamma function is defined by <math>\Gamma(t) = \int\limits_{0}^{\infty} x^{t-1} e^{-x} dx</math>. |

− | When the value of | + | 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 | *This function will give the result as error when | ||

− | 1. any one of the argument is | + | 1. any one of the argument is non-numeric. |

− | 2. | + | 2. Number is negative |

− | 3. | + | 3. If DegreeOfFreedom1<1 or DegreeOfFreedom2><math>10^{10}</math> and DegreeOfFreedom2<1 or DegreeOfFreedom2> <math>10^{10}</math> |

+ | |||

+ | ==ZOS== | ||

+ | |||

+ | *The syntax is to find FDIST in ZOS is <math>FDIST (Number,DegreeOfFreedom1,DegreeOfFreedom2)</math>. | ||

+ | **<math>Number</math> is the value of the function. | ||

+ | *For e.g.,FDIST(85.2,22,18) | ||

+ | *FDIST(67..70,6,8) | ||

==Examples== | ==Examples== | ||

− | #FDIST(20.6587,7,3)=0.01526530981 | + | #=FDIST(20.6587,7,3) = 0.01526530981 |

− | #FDIST(70.120045,12.2,6.35)=0.000011229898 | + | #=FDIST(70.120045,12.2,6.35) = 0.000011229898 |

− | #FDIST(10,1.3,1.5)=0. | + | #=FDIST(10,1.3,1.5) = 0.12923064798773362 |

− | #FDIST(-28,4,6)= | + | #=FDIST(-28,4,6) = #N/A (NUMBER > 0) |

+ | ==Related Videos== | ||

+ | {{#ev:youtube|7rGAh_XDvY8|280|center|F Distribution}} | ||

==See Also== | ==See Also== | ||

*[[Manuals/calci/FINV | FINV ]] | *[[Manuals/calci/FINV | FINV ]] | ||

− | *[[Manuals/calci/FTEST | FTEST ]] | + | *[[Manuals/calci/FTEST | FTEST ]] |

+ | |||

+ | ==References== | ||

+ | [http://en.wikipedia.org/wiki/F-distribution F-Distribution] | ||

− | + | *[[Z_API_Functions | List of Main Z Functions]] | |

+ | |||

+ | *[[ Z3 | Z3 home ]] |

## Latest revision as of 09:10, 2 June 2020

**FDIST (Number,DegreeOfFreedom1,DegreeOfFreedom2)**

- is the value of the function
- and are numbers of degrees of freedom.
- FDIST(), 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 is the value of the function , is the numerator degrees of freedom and 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:

where is the Gamma Function.

- The gamma function is defined by .

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> and DegreeOfFreedom2<1 or DegreeOfFreedom2>

## ZOS

- The syntax is to find FDIST in ZOS is .
- is the value of the function.

- For e.g.,FDIST(85.2,22,18)
- FDIST(67..70,6,8)

## Examples

- =FDIST(20.6587,7,3) = 0.01526530981
- =FDIST(70.120045,12.2,6.35) = 0.000011229898
- =FDIST(10,1.3,1.5) = 0.12923064798773362
- =FDIST(-28,4,6) = #N/A (NUMBER > 0)

## Related Videos

## See Also

## References