# Sum of inverse chi squared random variables

Let $X$ and $Y$ be two i.i.d. random variables that follow an inverse chi squared distribution. Let $\nu$ be the corresponding degrees of freedom parameter.

What is the distribution of the sum $S=X+Y$ ?

Update: Here we use the following definition:

$$\text{PDF}= \frac{1}{\Gamma(\nu /2)}2^{-\nu/2 }x^{-\nu/2-1} e^{-1/(2x)}$$

• Can you start by providing the definition (functional form) for your inverse chi-squared distribution. There are multiple competing definitions in the literature. – wolfies Dec 20 '15 at 15:49
• @wolfies Question updated. Thank you for your comment! – din Dec 20 '15 at 16:14