ksdensity default bandwidth value

Hi,

Does any one knows how matlab computes the default bandwidth in the function ksdensity?

Thank you very much,

Answer 1

[FK]

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 .

[Maximiliano Barbosa]

thank you, actually I was study how to obtain the default bandwith too

[Thomas]

Hi FK, I can reproduce the results if the MAD is > 0. If it is zero, MATLAB seems to use something else. Any idea what that could be?

Answer 2

[Ghada Saleh]

Hello Alexandra,

In MATLAB, the default bandwidth in 'ksdensity' function is calculated using the following formula:

BandWidth = sig * (4/(3*N))^(1/5);

where 'sig' is an estimated value of the standard deviation of the samples.

I hope this helps,

Ghada

[Alexandra]

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.

Answer 3

[Mohammad Khatamirad]

you can try this: [f, xi, bw] = ksdensity(X); bw = 'gives you the default bandwidth'