# Sum of two Von Mises random variables

I know that the sum of two independent normally distributed random variables is also a normal random variable, but is this true of other distributions? For example, what probability distribution does the sum of two Von Mises distributions follow?

• I think that @psboonstra means that if you sum two Von Mises deviates, $x$ and $y$, ignoring the fact that they are supposed to be circular, the range of $z=x+y$ is $[-2\pi,2\pi]$, not $[\pi,\pi]$. – sammosummo Dec 24 '19 at 17:50
• Perhaps--but that's irrelevant to demonstrating the sum does not have a von Mises distribution. For the von Mises distribution the sum must be computed modulo $2\pi.$ – whuber Dec 24 '19 at 18:34
• Yes, you are correct @whuber. Thank you for correcting me. I was working from the Wikipedia article which states that the support can be chosen to be any length-2$\pi$ radiatns interval, but I see now that the typical assumption is that the support is equal to $[-\pi, \pi]$. – psboonstra Dec 27 '19 at 16:42