Let's say I have some set of data which is not a "normal" distribution of data, meaning it does not hold a Gaussian, exponential, or other neat formulaic look. Here's an example of data where the PDF I want to create is based on the solid black line, within the red vertical lines:
Given that I already have the data, how can I create a PDF for this?
Next, I want to compare the data represented by the blue dots, and test whether it will look like the black line if I add some parameter. Say the black line is represented by $F(x)$ and the blue dots are represented by $G(x)$. I want to test:
$G(x) = P1*F(x)$
And I'd like to know what P1 is such that it is the best fit.