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Def: X has chi-square distribution with r degree of freedom if it has a gamma distribution with $\theta=2$ and $\alpha =\frac{r}{2}$, i.e. $f(x)=\frac{1}{\Gamma(\frac{r}{2})} 2^{\frac{r}{2}} x^{\frac{r}{2}-1} e^{\frac{-x}{2}}$, x>0. This is abbreviated by saying $X \sim\chi^2(r)$.

How is Chi square different than Gamma distribution in problem solving?

StubbornAtom
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shine
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    You are correct that each chi-squared distribution is a special case of a gamma distribution. What makes chi-squared distributions interesting is that they occur (e.g., in statistics) as sums of squares of independent standard normal random variables. – angryavian Mar 08 '20 at 00:19
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    It is look like this: Uniform $(0,1)$ distribution is special case of beta $(a,b)$ with $a=b=1$ (also beta is special case of Dirichlet ) so what .... another example: Exponential distribution is special case of ...... I think All of this because we develop(extend) them again and again. – Masoud Mar 09 '20 at 15:40
  • @masoud I see, thanks for drawing connections – shine Mar 09 '20 at 16:59

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