How to interpret a dataset with a pseudo-logarithmic trend?

I am dealing with a scatterplot where I am trying to figure out the relationship between two variables, but I have so far failed to identify what the best fit could be. The presence of zero values prevents me from using exponential and power law regression lines.

Zero values are not shown as the Y axis starts from 1, but they are present. My bad.

This is the scatterplot. To me it looks like this is some sort of logarithmic trend but I am not sure about it.

What model will best interpret this trend?

• you can try local smoothing if you can't remove the entries where Y=0 – Bach Mar 4 '16 at 13:10
• It seems that there is some limiting behaviour, first that values of $X$ cannot exceed $100$ (meaning $100$%?) and second that values of $Y$ tend to $0$ sharply as $X$ tends to its upper limit. Please confirm (or rebut). Note my advice (in a thread also started by you) stats.stackexchange.com/questions/184247/… to work with some transformation that stretches the far tail of $X$, at least for visualization. Subject-matter knowledge on what makes sense is crucial here; anonymising the data as $Y$ and $X$ just obscures key context. – Nick Cox Mar 4 '16 at 14:39
• Indeed there are limits: X cannot exceed 100 and Y stretches from 0 to nearly 4. These quantities would be hard to made sense of even if they were not "disguised". But the focus is on the trend itself, rather than the data. What do you think of an Asymptotic Concave Regression? – FaCoffee Mar 4 '16 at 14:44
• $4 [(100 - X)/100]^{1/20}$ might give an idea. – Nick Cox Mar 5 '16 at 0:32
• I'd certainly recommend working with $100 - X$ rather than $X$. – Nick Cox Mar 5 '16 at 7:06