Integrate kernel probability distribution function

Dear MatLab comunity,

I have a distribution of dihedral angles over a number of frames from a simulation. (attached is the data file)

M2OH6 = load('OH6p.txt');
y6 = M2OH6(:,2);

nbins = 100;
rng('default')
[f3,y6i] = ksdensity(y6);
plot(y6i,f3,'Color','r','Linewidth',1)
xlabel('\theta (deg)');
ylabel('P(\theta) (deg^{-1})');
xticks(-360:60:360);
yticks(0:0.01:0.045);
axis([-360 360 0 0.045]);
pbaspect([1 1 1]);

So I need to know what is the percentage of the states falling in the range between let's say 0:120 degrees (theta), 120:180 degrees and 180:-120.

In such case I was thinking that maybe I should integrate the kernel density function in such ranges but I'm not sure how to do it and obviously I'm a very beginner in MatLab.

Is there anybody who could suggest me a way?

Thanks in advance,

Alex

Answer 1

[Peng Li]

https://www.mathworks.com/help/matlab/ref/trapz.html

trapz is a function that deals with numerical integration. Check the above link for details.

Answer 2

[Jeff Miller]

If you just want to know the percentages in various ranges, it seems easier to tabulate the scores directly than to mess about with ksdensity. What about just something like:

M2OH6 = load('OH6p.txt');
y6 = M2OH6(:,2);
binEdges = [-180 -120 0 120 180];  % set the boundaries to isolate the bin ranges you are interested in
counts = histcounts(y6,binEdges);  % count the number of scores in each range
pcts = counts / length(y6)*100     % convert to percentages

the first pcts value will be the % between -180 and -120, the second between -120 and 0, etc. Obviously you can set the bin edges whereever you want them.