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

I forgot to say what the distribution was. From Wikipedia:

In probability and statistics, the Bates distribution, named after Grace Bates, is a probability distribution of the mean of a number of statistically independent uniformly distributed random variables on the unit interval.