I am currently trying to understand how distributions emerge out of a simple calculation when combining data which have other distributional properties. What I mean with this is, as I am not a mathematician, is the following: Let's assume the following two equations

$\phi_{i,t}= \frac{S_{i,t}-C_{i,t}}{A_{i,t}}$ or $\phi_{i,t}=\frac{I_{i,t}}{A_{i,t}}$ where $S$ and $A$ are positive, $C$ is negative and $I$ can be positive and negative, too.

If I now plot the probability density function (PDF) over all $i$ in $t$ for the different variables and calculate $\phi$ a new "smoothed" distribution occurs. The plots look as follows: Plots

As I am not that familiar with the dynamics and properties lying behind that kind of process I would be very glad if someone could explain it to me or give me a hint where to look for the relevant literature.

Thank you in advance! Best, Alex