kernel-density | Multivariate kernel density estimation

Since you need to do some maths on the density curves to work out where the 95% intervals are, it is best to do this outside ggplot. I often find that people run into problems because they try to get ggplot to do too much of their data wrangling and summarizing. It is often easier to work out what you want to plot, then plot it.

In your case, your x and y co-ordinates already represent densities. For each Electrode, you just need to create a logical vector that tells you when the integral of the density is between 0.025 and 0.975, so that you can easily subset out the 95% confidence interval. You can do that using the split-aplly-bind method like this:

The easiest thing to do is build another figure fig2 with curve_type = 'normal' and pick up the values from there using:

By definition, an inflection point is the point where the second derivative of the function equals zero. In the practice, this means that an inflection point will be a point where the slope passes from increasing to decreasing, or v.v. Using this definition, I came with this approximate and non-automatic approach: Let's say that you have a dataframe, that I will call all, which contains the x-values in the first column, and the result of the density computation in the second one. From this dataframe, we can calculate the slope of two consecutive points like this :