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).
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 
.
.
