Changes

*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.

   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==