x = randn(100000,1);
[counts,binCenters] = hist(x,100);
binWidth = diff(binCenters);
binWidth = [binWidth(end),binWidth]; % Replicate last bin width for first, which is indeterminate.
nz = counts>0; % Index to non-zero bins
frequency = counts(nz)/sum(counts(nz));
H = -sum(frequency.*log(frequency./binWidth(nz)))
It seems that the most common references (i.e. Wikipedia!) are assuming a discrete random variate (with a specified probability mass function), rather than a discrete approximation to a continuous variate. In that case, the "bin width" is effectively 1. Here is a reference that discusses the case of non-unit bin width, and has the formula that I used as the basis of the above calculation: http://www2.warwick.ac.uk/fac/soc/economics/staff/academic/wallis/publications/entropy.pdf
