Hi guys,
I encountered decreasing values of the estimated cumulative distribution function when using ksdensity. I think this should not be possible, since F(x1,x2) is defined to be non-decreasing (see e.g. https://en.wikipedia.org/wiki/Cumulative_distribution_function#Multivariate_case). Why can ksdensity return decreasing values?
This is a minimum code example:
rng default % for reproducibility
x = [0+.5*rand(20,1) 5+2.5*rand(20,1); .75+.25*rand(10,1) 8.75+1.25*rand(10,1)];[F,xi] = ksdensity(x,'function','cdf');figureksdensity(x,xi,'function','cdf');xlabel('x1');ylabel('x2');zlabel('F(x1,x2)');title({'Problem: Decreasing cumulative distribution function', ... 'e.g. F(x1=0,x2=11) > F(x1=0,x2=13)'});
Which plots this:
Best Answer