Difference between revisions of "Manuals/calci/FDIST"
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(Created page with "<div id="6SpaceContent" class="zcontent" align="left"> '''FDIST'''('''x''', '''DF1''', '''DF2''') '''Where X''' is the value at which to evaluate the function, '''DF...") |
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| − | <div | + | <div style="font-size:30px">'''FDIST (Number,DegreeOfFreedom1,DegreeOfFreedom2)'''</div><br/> |
| + | *<math>Number</math> is the value of the function | ||
| + | *<math>DegreeOfFreedom1</math> and <math>DegreeOfFreedom2</math> 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 <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. | ||
| + | *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>0<x<\infty</math> where <math>\Gamma</math> is the Gamma Function. | ||
| + | *The gamma function is defined by <math>\Gamma(t) = \int\limits_{0}^{\infty} x^{t-1} e^{-x} dx</math>. | ||
| + | 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><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== | |
| + | #=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== | |
| − | + | {{#ev:youtube|7rGAh_XDvY8|280|center|F Distribution}} | |
| − | |||
| − | + | ==See Also== | |
| + | *[[Manuals/calci/FINV | FINV ]] | ||
| + | *[[Manuals/calci/FTEST | FTEST ]] | ||
| − | + | ==References== | |
| + | [http://en.wikipedia.org/wiki/F-distribution F-Distribution] | ||
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| − | + | *[[Z_API_Functions | List of Main Z Functions]] | |
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| − | + | *[[ Z3 | Z3 home ]] | |
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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.
is the value of the function
and 
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 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:
is the value of the function ,where is the Gamma Function.
^{\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}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/png/bf128c19052b2d77e9867508e60f25c553dfee41)
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>
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