I have a point cloud (2D for now) of $N$ normally distributed points (with a certain $\sigma$).
My first question would be how the pairwise distance distribution looks (just by chance I discovered a normal distribution folded by the error function does the job well in fitting the distance distribution, but I have problems in quantifying the parameter like normalization factor).
The second question (probably easy if the first part is solved): I now have a second point cloud nearby (distance $d$ to the first cloud, also normal distribution, same $\sigma$, $N_2$ number of points). How does that change the distribution (that now of course has an additional peak).
Any input is appreciated. Thanks a lot (this is my first post - I am sorry if I posted this incorrectly)!
Below you find links to images of the distribution for an example population (the fit in the second picture is just two gauss folded with an error function - as mentioned: this fits nicely but I am not sure about the parameter relation).
point cloud: https://i.stack.imgur.com/NsGHA.png
pdist histogram: https://i.stack.imgur.com/5IIMC.png