I realize this does not make sense what I'm trying to do below *. So I am rephrasing: I have data that takes on values from [-1,1] heavily centred around zero, say distributed Gaussian about 0. I have other data that goes from [1,2.5] but distributed as an inverse curve say 1/x^2.
If I am multiplying individual data points' values, they will span [-2.5,2.5], but how will they be distributed? It does not seem I can just fit two curves and multiply them. Should I make two distributions for a large number of data and then just multiply and fit? there seems there should be an analytical approach.
Make sense?
* I have two variables with distributions. The first (A) will be something like a unit Gaussian centred on zero, taking values in x -1 to +1, but noisy. The second (B) looks like a steep inverse function, say taking values from x = 1, y=1 to x= 2.5, y=very close to zero descending monotonically along the x-axis. I want to multiply these and see what my distribution would look like. Is it simply gaussian*(1/x^a)? I know the bounded function would have unit height and domain -2.5 to 2.5, but is that all there is to it? Is there a way to better describe it's shape mathematically? See the attached image. distribution
Thanks in advance
No bites?
I think that I can do this to accomplish the same, though it is not the exact same thing. I can multiply the Pareto (https://en.wikipedia.org/wiki/Pareto_distribution) or shifted chi-sqr, or ... distributions, and regenerate the numbers.