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>> x = [randn(30,1); 5+randn(30,1)];
>> [f,xi] = ksdensity(x);
>> sum(f)

ans =

    5.5376

I ran the ksdensity function in MATLAB above. After getting the density values, I summed them up. I've got 5.5376, but I expected 1. What am I missing here? Is there any good introductory book that explains the mechanics of the kernel density estimation in line with the ksdensity function?

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  • $\begingroup$ This question seems to come down to a misunderstanding of densities, which is addressed at stats.stackexchange.com/questions/4220. Does that solve your problem? $\endgroup$ – whuber Oct 6 '14 at 23:32
  • $\begingroup$ Thank you very much, whuber. Confusing, but I will dig in. $\endgroup$ – Bill TP Oct 6 '14 at 23:44
  • $\begingroup$ You appear to be summing the height of the density at some collection of values. Why would that sum to 1? $\endgroup$ – Glen_b Oct 7 '14 at 1:55
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it integrates to one, not sums to one.

trapz(xi, f) should return something close to 1.

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