The 'ksdensity' function uses "Silverman's rule" as given in the post of Ghada. The difference between the calculations of Alexandra and the calculations done in Matlab is caused by a different estimation of the the standard deviation. Instead of estimating it by it is done by applying a more robust estimator with (see this Wikipedia article for further information).
With m=[1,3,2,5] you can derive with Silverman's rule that the default bandwith is given by .
I have used this formula to test the calculations of the bandwidth and I don't think it is correct.
Take a simple example: m=[1,3,2,5] Then from [a,b,c]=ksdensity(m,m,'function','cdf') c=1.1901 and sig*(4/(3*4))^(1/5)= 1.3709 So they don't yield the same answers.
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