Given a uniformly spread list of points as input, I am trying to get a function that maps those points onto the highest sections of a graph. Here is a picture of f(x) and the kind of distribution I want to get from the points
The way I've seen people say to to do this so far is to transform f(x) into a proability density function (PDF), then into a cumulative distribution function (CDF) by integrating the PDF from -infinity to x. After that, get the inverse of the CDF (quantile) and plug in points to that function. I've tried this and it does not seem to work.
https://www.desmos.com/calculator/w4qkxam5uw Here's the graph I'm doing this on, and I can get the CDF, but after that I do not know how to get the inverse CDF. The built-in quartile() function does not seem to work either, and instead does pretty much the same thing as the CDF, but with a list as far as I can see.
The image above shows the CDF (red line) and a sample of what the inverse CDF should be doing (mapping the points onto the line). If anyone knows how to get the inverse CDF, or how to properly use the quartile function, I would very much appreciate help because I've been stuck researching this for like 4 hours.