Difference between revisions of "Manuals/calci/FDIST"

From ZCubes Wiki
Jump to navigation Jump to search
Line 10: Line 10:
 
*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,r1,r2)=Γ[(r1+r2)/2](r1/r2)^r1/2*(x)r1/2-1/ Γ(r1/2)Γ(r2/2)(1+r1x/r2)^(r1+r2)/2,  0<x<\infty</math> where Γ is the gamma function.
+
<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 Γ is the gamma function.
 
*The gamma function is defined by  Gamma(t) = integral 0 to infinity  x^{t-1} e^{-x} dx.   
 
*The gamma function is defined by  Gamma(t) = integral 0 to infinity  x^{t-1} e^{-x} dx.   
 
When the value of df1 and df2 are not integers ,then it is converted in to integers.
 
When the value of df1 and df2 are not integers ,then it is converted in to integers.
Line 17: Line 18:
 
   2.x is negative
 
   2.x is negative
 
   3. df1 or df2<1 ,and  df1 ordf2>=10^10
 
   3. df1 or df2<1 ,and  df1 ordf2>=10^10
 
  
 
==Examples==
 
==Examples==

Revision as of 01:12, 8 January 2014

FDIST(x,df1,df2)


  • is the value of the function
  • and is 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:

0<x<\infty</math> where Γ is the gamma function.

  • The gamma function is defined by Gamma(t) = integral 0 to infinity x^{t-1} e^{-x} dx.

When the value of df1 and df2 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 nonnumeric.
 2.x is negative
 3. df1 or df2<1 ,and  df1 ordf2>=10^10

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


See Also


References