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

Question

Andreas Haselsteiner 2017-3-31

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/332994-why-does-bivariate-ksdensity-return-decreasing-cdf-values

编辑： Oskar Adolfson 2017-11-28

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)'});