how to estimate cdf from ksdensity pdf

Question

jenka 2018-11-14

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https://ww2.mathworks.cn/matlabcentral/answers/429916-how-to-estimate-cdf-from-ksdensity-pdf

评论： Star Strider 2018-11-14

I have a quick question about ksdensity. For a given variable I derive distribution by binning into a specified number of bins, calculating the number of samples in each bin. For example, I used 10 bins to get the pdfs

To sample distributions, those pdf's are converted to cdf's, I draw random values from 0-1 so sample that cdf at bin center i. This allows to only get back the values at each bin center which for contionous variable is not what I want. Thus I then sample uniformatly from i-1 to i+1.

I was wondering if I can used ksdensity to do this as the more robust soluton. So essentially finding CDF from PDF that was estimated using Kernel Desnity?

Thank you!

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Answer 1

Star Strider 2018-11-14

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/429916-how-to-estimate-cdf-from-ksdensity-pdf#answer_346986

在 MATLAB Online 中打开

There is an option for ksdensity to return the cdf:

x = [randn(30,1); 5+randn(30,1)];
[f,xi] = ksdensity(x);
figure
plot(xi,f)
grid
title('PDF')
[f,xi] = ksdensity(x, 'Function','cdf');
figure
plot(xi,f)
grid
title('CDF')

Experiment with your own distribution. This is discontinuous, so you may need to use the interp1 function for intermediate values.

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jenka 2018-11-14

actually, I think this might work:

x = [randn(30,1); 5+randn(30,1)];
[f,xi] = ksdensity(x);
% Generate uniform random number between 0 and 1
ur =  rand(m,n);
% Interpolate ur from empirical cdf and extraplolate for out of range
% values.
xr = interp1(xi,f,ur,[],'extrap');

Star Strider 2018-11-14

在 MATLAB Online 中打开

O.K. I am not certain what m and n are, and without more information, I continue to guess at the appropriate solution. I alluded (and linked) to interp1 earlier.

You can calculate the probabilities, then weight them appropriately.

Example —

rn = repelem(xi, fix(f/min(f)));                    % Generate Random Values
figure
histogram(rn, numel(f))                             % Plot Histogram

That will reproduce the PDF of the distribution.

Experiment to get the result you want.

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