Probability Density Function using ksdensity is not normalized

I have a vector "columnA" of N data points. I want to find the PDF. I use:

xi = min(columnA):1e-9:max(columnA);
f = ksdensity(columnA,xi);
plot(xi,f)

But when I use trapz to integrate f:

trapz(f)/length(xi)

the value is too far from 1. Even when increasing the range of xi, I still do not get reasonable value.

[Ali]

Any idea?

Answer 1

[VladTheInstaller]

Actually, the output from ksdensity is normalized, but you will have to use numerical integration along the appropriate space. In your case,

   trapz(xi,f)

should be close to 1.

Answer 2

[Image Analyst]

Why not use hist() or histc() to get the histogram? The histogram is essentially the probability density function.

Answer 3

[Youssef Khmou]

The ksdensity produces a Probability density function, no need to divide by the length of the x vector :

   x=randn(200,1);
   y=[min(x):0.1:max(x)];
   p=ksdensity(x,y);
   sum(p)
   % plot(y,p)