difference between trapz and just summing

Dear everybody, I was wondering what is the difference between the function trapz and the sum as used below. It appears to be about the same. I am just trying to find the intersection between two histograms:

h = [16, 45, 23, 1] 
g = [18, 38, 27, 5] 
hn = h./sum(h);
gn = g./sum(g);

intersection = trapz(min([hn;gn]);  
intersection = sum(min([hn;gn]));

Which one would be favorable over the other. It appears trapz should be better approximation.

Answer 1

[Matt J]

If the function you've sampled and are integrating is piece-wise constant, then summing its samples will be ideal. If instead, it is piece-wise linear, the trapezoidal approximation will be ideal. You have to decide which situation more accurately describes your function.