why my kernel density function never touches x axes?

Hello:

I want plot kernel density function with the attached test data. I have used foll. code:

Xgrid1 = linspace(min(X),max(X),1000);
pdfEst_1 = ksdensity(X,Xgrid1,'function','pdf');    
plot(Xgrid1,pdfEst_1,'Color','B','linew',1.8);   

However, the generated density function never touches the x-axes & always moves up, without any closed bounds. Any possible ways that the generated PDFs touches x - axes?

[the cyclist]

Can you upload a file with H_10?

[Poulomi Ganguli]

sorry, that H_10 is actually X, I have edited it.

[the cyclist]

Is that what is in the file Test1? Just those 15 data points?

It will depend on the kernel you choose, but the estimated density will be zero (or approach zero) as you move away from where the function has support. You haven't defined any grid points that are far away from where X has support.

[Poulomi Ganguli]

Got it. Thanks!

Answer 1

[the cyclist]

Now that we've clarified some things, let me capture my reply in an actual answer.

The issue is that you have defined your X range to cover only places where the estimated PDF has support, because you actually have some data there. If, instead, you extend the range far enough away from the data, then the estimated PDF will go to zero (or at least approach zero).

For example:

extendRange = (max(X)-min(X))/2;
Xgrid1 = linspace(min(X) - extendRange,max(X) + extendRange,1000);
pdfEst_1 = ksdensity(X,Xgrid1,'function','pdf');    

figure
plot(Xgrid1,pdfEst_1,'Color','B','linew',1.8);

Exactly how far out you need to go will depend on the kernel you choose for ksdensity.