# ksdensity default bandwidth value

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Alexandra 2015 年 8 月 5 日
Hi,
Does any one knows how matlab computes the default bandwidth in the function ksdensity?
Thank you very much,

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### 回答 (3 件)

Ghada Saleh 2015 年 8 月 7 日
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,
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Alexandra 2016 年 3 月 14 日
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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FK 2022 年 1 月 22 日
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 .
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Maximiliano Barbosa 2022 年 10 月 4 日
thank you, actually I was study how to obtain the default bandwith too

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

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