I have been playing with MacOS’s grapher application. It is free and works really well, to understand the Bates distribution (compared to Normal / Gaussian).
As an intermediate step I plotted the following which I find quite cute:
Here is the normal distribution plotted against the Bates distribution.
Here are the two equations and the plot params (we used n= 4
The plot goes wild for x>1 or x<1 – it almost looks chaotic.
Here it is again for n=7