# Negative values in kernel density estimation

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Sunetra Chituru on 26 Sep 2022
Commented: Sunetra Chituru on 6 Oct 2022
My input data vector 'x' has values ranging between 20 to 500 . when i use the command
[f1,y1]= ksdensity(x),
the out put values are negative. how is this possible?
##### 2 CommentsShowHide 1 older comment
Sunetra Chituru on 30 Sep 2022
I have attached the excel sheet containing the data.

the cyclist on 4 Oct 2022
(Sorry for the delayed response. I didn't get a notification that you had replied to my comment.)
The K-S density looks like a pretty appropriate fit to me, and your data are indeed skewed. I don't see an issue.
% Pull the data from the table into a numeric array, for convenience
x = tbl.Var1;
% Fit the K-S density, assuming support for only positive values
[f1,y1]= ksdensity(x,"Support","positive");
% Plot that fit against a histogram of the data
figure
hold on
histogram(x,10:20:210,"Normalization","pdf")
h = plot(y1,f1);
set(h,"LineWidth",2)
legend(["Binned data","K-S density"])
Sunetra Chituru on 6 Oct 2022
Hi,
thanks for the response.

Bala Tripura Bodapati on 30 Sep 2022
Hi Sunetra
It is my understanding that the output values returned by 'ksdensity' function are negative though the input vector contains positive values.
A 'normal kernel function' is the default function used by ‘ksdensity' function to return the probability density estimate. If your data has values near zero, you'll naturally get some overlap into the negative side as the individual kernels are summed.
As a workaround, the 'support' property can be set to 'positive' to restrict the density to positive values. The following code illustrates the suggested workaround:
x=20:10:500
[f1,y1]= ksdensity(x,'support','positive')
plot(y1,f1)
Sunetra Chituru on 30 Sep 2022
Hi Tripura,
Thanks for the response. I have implemented the support property , but the distribution obtained seems to be much more skewed when compared to my distribution obtained without the support function. Moreover the values in my data are not anywhere near to zero.

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