Is there a closed form CDF for the sum of two triangularly distributed random variables? To calculate the PDF of the sum of two triangularly distributed random variables all I did was add them together and divided by two:
$\dfrac{f(x, a1, b1, c1) + f(x, a2, b2, c2)}{2}$

And implementing it in Python gets me the following PDF:

My issue was with the CDF. Addition doesn't work, but I don't know how to mathematically derive a closed form for it:


You need to do a Fourier convolution.
For x distributed according to g(x), and y distribution according to h(y), the pdf of z=x+y is given by the attached image.
(Side note for product of variables z=x*y, you would need to do a Mellin convolution).

