Why does (bivariate) ksdensity() return decreasing cdf values?

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');

figure
ksdensity(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:

Answer 1

[Oskar Adolfson]

This is a known bug which was fixed in the R2017b MATLAB version. Anyone using R2017b or newer versions shouldn't encounter this problem anymore.