# Fitting right skewed data using maximum likelihood models?

I have this data that predicts female for increasing number of females (x-axis). Currently, I have fit a regular quadratic function, however it does not seem to estimate it well.

I want to fit a curve that peaks on the left of the graph (left skewed) with a long, right tail to this data and estimate the peak of the curve (See this curve for example). I also want to compare it to the regular quadratic to show that its a good fit. However, I'm not sure what equation would best represent the data here?

• Could you clarify for us what a "left skewed (right tailed) curve" is intended to be? – whuber May 15 at 21:16
• I have commented to clarify the question. Does that help? – Biotechgeek May 15 at 21:19
• It does--although that's a truly unusual use of "left skewed." But the plot clearly shows that such a curve would be a bad fit, so why do this? Moreover, if by definition such a curve "peaks on the left," then the peak is at 0 by definition, so why is any estimation needed? – whuber May 15 at 21:20
• It is to do with the biology of the organism. I understand from other studies that female size is density dependent, where when there are fewer females the size goes up..and as it gets more crowded it decreases. However, this trend maybe tightly clustered on the left side – Biotechgeek May 15 at 21:23
• I find that confusing, because the curve you are fitting has little if anything to do with density or with clustering (although "skewness" does) and I'm unable to make sense of your characterization that it "predicts female for increasing number of females." It makes me worry that you might not accurately be describing what you really need to do. Let me confirm: are you trying to find how female size might be related to the number of females? – whuber May 15 at 21:44