I have a bunch of particles spread over a 2D area. I plan to fit a a distribution to describe the spread.
To start off :
I have about 100 particles arranged in a circular pattern in a "unit" consisting of 10 pieces ( like a pizza basically ). There are then 10 of these "units" arranged in a cylindrical shape all contained in a cylindrical shell.
A charge ignites at the back of the cylinder, sending the projectiles forward.
My argument is that the front pieces will be pushed by the rear ones, and result in a higher spread for the first 2-3 rows, whereas the last few rows will see a tighter spread as there are no particles "pushing" them out of the way.
If I were to draw a scatter plot of the spread, it would be slightly concentrated in the middle and increase from there to a point and then drop off.
I estimate it to look something like this if I were to view a line from the centre to the edge:
This distribution will then be rotated around the centre to from a kind of "doughnut" shape that is raised more in the centre than the sides.
Now the problem I have :
What do I call a distribution like this? What is the general formula for this type of distribution? It seems like a normal distribution with a twist.